(iii)Let E be an event of getting no tails. Favourable outcomes = HH Number of favourable outcomes = 1 P(E) = 1/4 Probability of getting no tails is 1/4 . (iv)Let E be an event of getting atmost one...
Two different coins are tossed simultaneously. Find the probability of getting :
Two different coins are tossed simultaneously. Find the probability of getting :
(i) two tails
(ii) one tail
Solution: When 2 coins are tossed, the possible outcomes are HH. HT, TH, TT. Number of possible outcomes = 4 (i)Let E be an event of getting 2 tails. Favourable outcomes = TT Number of favourable...
Two coins are tossed once. Find the probability of getting:
(i) 2 heads
(ii) at least one tail.
Solution: When 2 coins are tossed, the possible outcomes are HH. HT, TH, TT. Number of possible outcomes = 4 (i)Let E be an event of getting 2 heads. Favourable outcomes = HH Number of favourable...
All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting
(iii) a black card
(iv) a heart
(iii) Let E be the event of getting a black card. There will be 23 black cards remaining since 3 spades are removed. Number of favourable outcomes = 23 P(E) = 23/49 Hence the probability of getting...
All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting
(i) a black face card
(ii) a queen
Solution: Total number of cards = 52-3 = 49. [since 3 face cards of spade are removed] So number of possible outcomes = 49. (i) Let E be the event of getting black face card. There will be 3 black...
A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:
(xi) neither a spade nor a jack
(xii) neither a heart nor a red king
(xi) Let E be the event of getting a neither a spade nor a jack. There are 13 spades and 3 other jacks. So remaining cards = 52-13-3 = 36 There will be 36 cards which are neither a spade nor a jack....
A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:
(ix) a non-ace
(x) non-face card of black colour
(ix) Let E be the event of getting a non ace card. There will be 48 non ace cards. Number of favourable outcomes = 48 P(E) = 48/52 = 24/26 = 12/13 Hence the probability of getting a non ace card is...
A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:
(vii) a black face card
(viii) a black card
(vii) Let E be the event of getting a black face card. There will be 6 black face cards. Number of favourable outcomes = 6 P(E) = 6/52 = 3/26 Hence the probability of getting a black face card is...
A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:
(v) a king or a queen
(vi) a non-face card
(v) Let E be the event of getting a king or a queen. There will be 4 cards of king and 4 cards of queen. Number of favourable outcomes = 4+4 = 8 P(E) = 8/52 = 2/13 Hence the probability of getting a...
A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. Find the probability that it is
(i) white
(ii) not red.
Solution: Total number of balls = 24 Number of red balls = x. Number of white balls = 2x. Number of blue balls = 3x. x+2x+3x = 24 6x = 24 x = 24/6 = 4 Number of red balls = x = 4 Number of white...
A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball is twice that of a red ball, find the number of balls in the bag.
Solution: Number of red balls = 6 Let number of blue balls be x. Total number of balls = 6+x Probability of drawing a red ball = 6/(6+x) Probability of drawing a blue ball = x/(6+x) Given the...
A bag contains 15 balls of which some are white and others are red. If the probability of drawing a red ball is twice that of a white ball, find the number of white balls in the bag.
Solution: Total number of balls in the bag = 15. Let the number of white balls be x. Then number of red balls = 15-x. The probability of drawing a white ball = x/15. Probability of drawing a red...
Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn at random from this box. Find the probability that the number on the card is
(iii) a number which is a perfect square
(iv) a prime number less than 30.
(iii) Let E be the event of getting the number on the card is a perfect square. Outcomes favourable to E are {4,9,16,25,36,49,64,81,100} Number of favourable outcomes = 9 P(E) = 9/100 Hence the...
Cards marked with numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn at random from this box. Find the probability that the number on the card is
(i) an even number
(ii) a number less than 14
Solution: The possible outcomes are {2,3,…101} Number of possible outcomes = 100 (i) Let E be the event of getting the number on the card is an even number. Outcomes favourable to E are...
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears
(i) a two-digit number
(ii) a perfect square number
(iii) a number divisible by 5.
Solution: The possible outcomes are {1,2,3,…90} Number of possible outcomes = 90 (i) Let E be the event of getting the number on the disc is a two-digit number. Outcomes favourable to E are...
Tickets numbered 3, 5, 7, 9,…., 29 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is
(i) a prime number
(ii) a number less than 16
(iii) a number divisible by 3.
Solution: The possible outcomes are {3,5,7,9..…29} Number of possible outcomes = 14 (i) Let E be the event of getting the number on the ticket is a prime number. Outcomes favourable to E are...
Cards marked with numbers 13, 14, 15, …, 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the card drawn is
(i) divisible by 5
(ii) a perfect square number.
Solution: The possible outcomes are {13,14,15,…60} Number of possible outcomes = 48 (i) Let E be the event of getting the number on the card is divisible by 5. Outcomes favourable to E are...
.A box contains 19 balls bearing numbers 1, 2, 3,…., 19. A ball is drawn at random from the box. Find the probability that the number on the ball is :
(iii) neither divisible by 5 nor by 10
(iv) an even number.
(iii) Let E be the event of getting the number on the ball is neither divisible by 5 nor by 10. Outcomes favourable to E are {1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19} Number of favourable outcomes =...
.A box contains 19 balls bearing numbers 1, 2, 3,…., 19. A ball is drawn at random from the box. Find the probability that the number on the ball is :
(i) a prime number
(ii) divisible by 3 or 5
Solution: The possible outcomes are {1,2,3,4…19} Number of possible outcomes = 19 (i) Let E be the event of getting the number on the ball is a prime number. Outcomes favourable to E are...
A box contains 15 cards numbered 1, 2, 3,…..15 which are mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is :
(iii) divisible by 3
(iv) divisible by 3 and 2 both
(iii) Let E be the event of getting the number on the card is divisible by 3. Outcomes favourable to E are {3,6,9,12,15} Number of favourable outcomes = 5 P(E) = 5/15 = 1/3 Hence the probability of...
A box contains 15 cards numbered 1, 2, 3,…..15 which are mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is :
(i) Odd
(ii) prime
Solution: The possible outcomes are {1,2,3,4…15} Number of possible outcomes = 15 (i) Let E be the event of getting the number on the card is odd. Outcomes favourable to E are {1,3,5,7,9,11,13,15}...
A box contains 25 cards numbered 1 to 25. A card is drawn from the box at random. Find the probability that the number on the card is :
(i) even
(ii) prime
(iii) multiple of 6.
Solution: The possible outcomes are {1,2,3,4 ….25} Number of possible outcomes = 25 (i) Let E be the event of getting the number on the card is an even number. Outcomes favourable to E are...
Cards marked with numbers 1, 2, 3, 4,…20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is
(i) a prime number
(ii) divisible by 3
(iii) a perfect square ? (2010)
Solution: The possible outcomes are {1,2,3,….20} Number of possible outcomes = 20 (i) Let E be the event of getting the number on the card is a prime number. Outcomes favourable to E are...
An integer is chosen between 0 and 100. What is the probability that it is
(i) divisible by 7?
(ii) not divisible by 7?
Solution: Number of integers between 0 and 100 = 99 Number of possible outcomes = 99 (i) Let E be the event of getting an integer divisible by 7. Outcomes favourable to E are...
Sixteen cards are labeled as a, b, c,…, m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is:
(i) a vowel
(ii) a consonant
(iii) none of the letters of the word median.
Solution: The possible outcomes are {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p} Number of possible outcomes = 16 (i) Let E be the event of getting a vowel. Outcomes favourable to E are { a,e,i,o} Number of...
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (shown in the adjoining figure) and these are equally likely outcomes. What is the probability that it will point at
(i) 8 ?
(ii) an odd number ?
Solution: The possible outcomes of the game are {1,2,3,4,5,6,7,8} Number of possible outcomes = 8 (i) Let E be the event of arrow pointing 8. Outcomes favourable to E is 8. Number of favourable...
A die has 6 faces marked by the given numbers as shown below: The die is thrown once. What is the probability of getting
(i) a positive integer.
(ii) an integer greater than – 3.
(iii) the smallest integer ?
Solution: When a die is thrown, the possible outcomes are {1,2,3,-1,-2,-3} Number of possible outcomes = 6 (i) Let E be the event of getting a positive integer. Outcomes favourable to E are {1,2,3}...
In a single throw of a die, find the probability of getting:
(vii) a number between 3 and 6
(viii) a number divisible by 2 or 3.
(vii) Let E be the event of getting a number between 3 and 6. Outcomes favourable to E is 4,5. Number of favourable outcomes = 2 P(E) = 2/6 = 1/3 Hence the probability of getting a number between 3...
In a single throw of a die, find the probability of getting:
(v) a number less than 8
(vi) a number divisible by 3
(v) Let E be the event of getting a number less than 8. Outcomes favourable to E is 1,2,3,4,5,6. Number of favourable outcomes = 6 P(E) = 6/6 = 1 Hence the probability of getting a number less than...
A die is thrown once. What is the probability that the
(i) number is even
(ii) number is greater than 2 ?
Solution: When a die is thrown, the possible outcomes are 1,2,3,4,5,6. So Sample space = { 1,2,3,4,5,6} Number of possible outcomes = 6 Even numbers are (2,4,6). Number of favourable outcomes = 3...
A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Peter, a trader, will only accept the shirts which are good, but Salim, another trader, will only reject the shirts which have major defects. One shirts is drawn at random from the carton. What is the probability that
(i) it is acceptable to Peter ?
(ii) it is acceptable to Salim ?
Solution: Total number of shirts = 100 Number of good shirts = 88 Number of shirts with minor defects = 8 Number of shirts with major defects = 4 Peter accepts only good shirts. So number of shirts...
A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. It is equally likely that one of the coins will fall down when the bank is turned upside down, what is the probability that the coin
(i) will be a 50 p coin?
(ii) will not be Rs 5 coin?
Solution: Number of 50 paisa coins = 100 Number of 1 rupee coins = 50 Number of 2 rupee coins = 20 Number of 5 rupee coins = 10 Total number of coins = 100+50+20+10 = 180 (i) Probability of getting...
A bag contains 6 red balls, 8 white balls, 5 green balls and 3 black balls. One ball is drawn at random from the bag. Find the probability that the ball is :
(iii) not green
(iv) neither white nor black.
(iii)Probability of not green = Probability of getting red, white and black = (6+8+3)/22 = 17/22 Hence the probability of not green is 17/22. (iv) Probability of neither white nor black =...
A bag contains 6 red balls, 8 white balls, 5 green balls and 3 black balls. One ball is drawn at random from the bag. Find the probability that the ball is :
(i) white
(ii) red or black
Solution: Number of red balls = 6 Number of white balls = 8 Number of green balls = 5 Number of black balls = 3 Total number of marbles = 6+8+5+3 = 22 (i)Probability of white balls, = 8/22 = 4/11...
A box contains 7 blue, 8 white and 5 black marbles. If a marble is drawn at random from the box, what is the probability that it will be
(iii) not black?
(iv) green?
(iii) Probability of not black = Probability of white and blue = (7+8)/20 = 15/20 = 3/4 Hence the probability of not black is 3/4. (iv) Since there are no green marbles in the box, the probability...
A letter is chosen from the word ‘TRIANGLE’. What is the probability that it is a vowel ?
Solution: Number of vowels in the word ‘TRIANGLE’ = 3 Total number of letters = 8 Probability that the letter chosen is a vowel , P(E) = 3/8 Hence the probability that the letter chosen is a vowel...
There are 40 students in Class X of a school of which 25 are girls and the others are boys. The class teacher has to select one student as a class representative. She writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of
(i) a girl ?
(ii) a boy ?
Solution: Total number of students = 40 Number of girls = 25 Number of boys = 40-25 = 15 (i) Probability of getting a girl, P(E) = 25/40 = 5/8 Hence the probability of getting a girl is 5/8. (ii)...
A bag contains 3 red balls and 5 black balls. A ball is drawn at random from a bag. What is the probability that the ball drawn is .
(i) red ?
(ii) not red ?
Solution: (i) Number of red balls = 3 Number of black balls = 5 Total number of balls = 3+5 = 8 Probability that the ball drawn is red , P(E) = 3/8 Hence the probability that the ball drawn is red...
Two players, Sania and Sonali play a tennis match. It is known that the probability of Sania winning the match is 0.69. What is the probability of Sonali winning ?
Solution: Probability of Sania winning the match, P(E) = 0.69 Probability of Sonali winning = Probability of Sania losing, = 1-0.69 = 0.31 Hence the probability of Sonali winning is...
If the probability of winning a game is 5/11, what is the probability of losing ?
Solution: Given probability of winning the game, P(E) = 5/11 We know that, Probability of losing game, = 1-5/11 = (11-5)/11 = 6/11 Hence the probability of losing game is 6/11.
In a lottery, there are 5 prized tickets and 995 blank tickets. A person buys a lottery ticket. Find the probability of his winning a prize.
Solution: Number of prized tickets = 5 Number of blank tickets = 995 Total number of tickets = 5+995 = 1000 The probability of winning a prize, P(E) P(E) = 5/1000 = 1/200 Hence the required...
A box contains 600 screws, one-tenth are rusted. One screw is taken out at random from this box. Find the probability that it is a good screw.
Solution: Total number of screws = 600 Number of possible outcomes = 600 Number of rusted screws = one tenth of 600 = (1/10)×600 = 60 Number of remaining good screws = 600-60 = 540 Number of...
A bag contains a red ball, a blue ball and a yellow ball, all the balls being of the same size. Anjali takes out a ball from the bag without looking into it. What is the probability that she takes out
(i) yellow ball ?
(ii) red ball ?
(iii) blue ball ?
Solution: Anjali takes out a ball from the bag without looking into it. So, it is equally likely that she takes out any one of them. Let Y be the event ‘the ball taken out is yellow’, B be the event...