Exercise 25C

### One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting: (v) a diamond or a spade

(v) Number of favorable outcomes for a diamond or a spade = 13 + 13 = 26 So, number of favorable outcomes = 26 Hence, P(getting a diamond or a spade) = 26/52 = 1/2

### One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting: (iii) the jack or the queen of the hearts (iv) a diamond

(iii) Favorable outcomes for jack or queen of hearts = 1 jack + 1 queen So, the number of favorable outcomes = 2 Hence, P(jack or queen of hearts) = 2/52 = 1/26 (iv) Number of favorable outcomes for...

### One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting: (i) a queen of red color (ii) a black face card

Solution: We have, Total possible outcomes = 52 (i) Number queens of red color = 2 Number of favorable outcomes = 2 Hence, P(queen of red color) = 2/52 (ii) Number of black cards = 26 Number of...

### A game consists of spinning arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; as shown below.If the outcomes are equally likely, find the probability that the pointer will point at: (v) a number less than or equal to 9 (vi) a number between 3 and 11

(v) Favorable outcomes for a number less than or equal to 9 are 1, 2, 3, 4, 5, 6, 7, 8, 9 So, number of favorable outcomes = 9 Hence, P(the pointer will be at a number less than or equal to 9) =...

### A game consists of spinning arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; as shown below.If the outcomes are equally likely, find the probability that the pointer will point at: (iii) a prime number (iv) a number greater than 8

(iii) Favorable outcomes for a prime number are 2, 3, 5, 7, 11 So, number of favorable outcomes = 5 Hence, P(the pointer will be at a prime number) = 5/12 (iv) Favorable outcomes for a number...

### A game consists of spinning arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; as shown below.If the outcomes are equally likely, find the probability that the pointer will point at: (i) 6 (ii) an even number

Solution: We have, Total number of possible outcomes = 12 (i) Number of favorable outcomes for 6 = 1 Hence, P(the pointer will point at 6) = 1/12 (ii) Favorable outcomes for an even number are 2, 4,...

### A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin: (i) will be a Re 1 coin? (ii) will not be a Rs 2 coin? (iii) will neither be a Rs 5 coin nor be a Re 1 coin?

(iii) Number of favourable outcomes for neither Re 1 nor Rs 5 coins = Number of favourable outcomes for Rs 2 coins = 50 = n(E) Hence, probability (neither Re 1 nor Rs 5 coin) = n(E)/ n(S) = 50/100 =...

### A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin: (i) will be a Re 1 coin? (ii) will not be a Rs 2 coin?

Solution: We have, Total number of coins = 20 + 50 + 30 = 100 So, the total possible outcomes = 100 = n(S) (i) Number of favourable outcomes for Re 1 coins = 30 = n(E) Probability (Re 1 coin) =...

### A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be: (iii) white or green?

(iii) Number of favorable outcomes for white or green ball = 16 + 8 = 24 = n(E) Hence, probability for drawing a white or green ball = n(E)/ n(S) = 24/34 = 12/17

### A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be: (i) not red? (ii) neither red nor green?

Solution: Total number of possible outcomes = 10 + 16 + 8 = 34 balls So, n(S) = 34 (i) Favorable outcomes for not a red ball = favorable outcomes for white or green ball So, number of favorable...

### The probability that two boys do not have the same birthday is 0.897. What is the probability that the two boys have the same birthday?

Solution: We know that, P(do not have the same birthday) + P(have same birthday) = 1 0.897 + P(have same birthday) = 1 Thus, P(have same birthday) = 1 – 0.897 P(have same birthday) =...

### A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is: (i) black (ii) red

Solution: We have, Total possible outcomes = number of red balls. (i) Number of favourable outcomes for black balls = 0 Hence, P(black ball) = 0 (ii) Number of favourable outcomes for red balls =...

### If P(E) = 0.59; find P(not E)

Solution: We know that, P(E) + P(not E) = 1 So, 0.59 + P(not E) = 1 Hence, P(not E) = 1 – 0.59 = 0.41

### Which of the following cannot be the probability of an event? (iii) 37% (iv) -2.4

(iii) As 0 ≤ 37 % = (37/100) ≤ 1 Thus, 37 % can be a probability of an event. (iv) As -2.4 < 0 Thus, -2.4 cannot be a probability of an event.

### Which of the following cannot be the probability of an event? (i) 3/7 (ii) 0.82

Solution: We know that probability of an event E is 0 ≤ P(E) ≤ 1 (i) As 0 ≤ 3/7 ≤ 1 Thus, 3/7 can be a probability of an event. (ii) As 0 ≤ 0.82 ≤ 1 Thus, 0.82 can be a probability of an...

### Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:(iii) less than or equal to 12

(iii) All the outcomes are favourable to the event E = ‘sum of two numbers ≤ 12’. Thus, P(E) = n(E)/ n(S) = 36/36 = 1

### Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is: (i) 8 (ii) 13

Solution: We have, the number of possible outcomes = 6 × 6 = 36. (i) The outcomes favourable to the event ‘the sum of the two numbers is 8’ = E = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)} The number...

### In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that: (i) it is acceptable to a trader who accepts only a good shirt? (ii) it is acceptable to a trader who rejects only a shirt with major defects?

Solution: We have, Total number of shirts = 50 Total number of elementary events = 50 = n(S) (i) As, trader accepts only good shirts and number of good shirts = 44 Event of accepting good shirts =...

### In a musical chairs game, a person has been advised to stop playing the music at any time within 40 seconds after its start. What is the probability that the music will stop within the first 15 seconds?

Solution: Total result = 0 sec to 40 sec Total possible outcomes = 40 So, n(S) = 40 Favourable results = 0 sec to 15 sec Favourable outcomes = 15 So, n(E) = 15 Hence, the probability that the music...

### 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

(iii) Number of black cards left = 23 cards (13 club + 10 spade) Event of drawing a black card = E = 23 So, n(E) = 23 Hence, probability of drawing a black card = n(E)/ n(S) = 23/49

### 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: We have, Total number of cards = 52 If 3 face cards of spades are removed Then, the remaining cards = 52 – 3 = 49 = number of possible outcomes So, n(S) = 49 (i) Number of black face cards...

### A box contains 7 red balls, 8 green balls and 5 white balls. A ball is drawn at random from the box. Find the probability that the ball is: (i) white (ii) neither red nor white.

Solution: We have, Total number of balls in the box = 7 + 8 + 5 = 20 balls Total possible outcomes = 20 = n(S) (i) Event of drawing a white ball = E = number of white balls = 5 So, n(E) = 5 Hence,...

### A and B are friends. Ignoring the leap year, find the probability that both friends will have: (i) different birthdays? (ii) the same birthday?

Solution: Out of the two friends, A’s birthday can be any day of the year. Now, B’s birthday can also be any day of 365 days in the year. We assume that these 365 outcomes are equally likely. So,...

### In a match between A and B: (i) the probability of winning of A is 0.83. What is the probability of winning of B? (ii) the probability of losing the match is 0.49 for B. What is the probability of winning of A?

Solution: (i) We know that, The probability of winning of A + Probability of losing of A = 1 And, Probability of losing of A = Probability of winning of B Therefore, Probability of winning of A +...

### From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is:(v) a card with number less than 8 (vi) a card with number between 2 and 9

(v) Numbers less than 8 = { 2, 3, 4, 5, 6, 7} Event of drawing a card with number less than 8 = E = {6H cards, 6D cards, 6S cards, 6C cards} So, n(E) = 24 Thus, probability of drawing a card with...

### From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is: (iii) a queen of black card (iv) a card with number 5 or 6

(iii) Event of drawing a queen of black colour = {Q(spade), Q(club)} = E So, n(E) = 2 Thus, probability of drawing a queen of black colour = n(E)/ n(S) = 2/52 = 1/26 (iv) Event of drawing a card...

### From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is: (i) a face card (ii) not a face card

Solution: We have, the total number of possible outcomes = 52 So, n(S) = 52 (i)  No. of face cards in a deck of 52 cards = 12 (4 kings, 4 queens and 4 jacks) Event of drawing a face cards = E = (4...

### A dice is thrown once. What is the probability of getting a number: (i) greater than 2? (ii) less than or equal to 2?

Solution: The number of possible outcomes when dice is thrown = {1, 2, 3, 4, 5, 6} So, n(S) = 6 (i) Event of getting a number greater than 2 = E = {3, 4, 5, 6} So, n(E) = 4 Thus, probability of...