(iii)Let E be an event of getting a sum divisible by 5. Favourable outcomes = {(1,4),(2,3), (3,2), (4,1),(4,6), (5,5), (6,4)} Number of favourable outcomes = 7 P(E) = 7/36 Probability of getting a...
Solution: When two dice are thrown simultaneously, the sample space of the experiment is {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1),(3,2), (3,3),...
Solution: When two dice are thrown simultaneously, the sample space of the experiment is {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1),(3,2), (3,3),...
Solution: Total number of cards = 52-4 = 48 [∵4 cards fell down] So number of possible outcomes = 48 (i) Let E be the event of getting black card. There will be 23 black cards since a black jack and...
(v) Let E be the event of getting a spade. There will be 10 spades. Number of favourable outcomes = 10 P(E) = 10/49 Hence the probability of getting a spade is 10/49. (vi) Let E be the event of...
(iii) Let E be the event of getting a king of red colour. There will be 2 cards of king of red colour. Number of favourable outcomes = 2 P(E) = 2/52 = 1/26 Hence the probability of getting a king of...
Solution: Total number of cards = 52. So number of possible outcomes = 52. (i) Let E be the event of getting ‘2’ of spades. There will be only one card of ‘2’ spades. Number of favourable outcomes =...
(v) Let E be the event of getting the number on the card is divisible by 3 or 2 Outcomes favourable to E are {2,3,4,6,8,9,10,12,14,15} Number of favourable outcomes = 10 P(E) = 10/15 = 2/3 Hence the...
Solution: There are 7 ways in which the month of February can occur, each starting with a different day of the week. (i)Only 1 way is possible for 5 Wednesdays to occur in February with 29 days....
Solution: For a leap year there are 366 days. Number of days in January = 31 Total number of January month types = 7 Number of January months with 5 Mondays = 3 (i)Probability that the month of...
(iii) Let E be the event of arrow pointing a number greater than 2. Outcomes favourable to E are {3,4,5,6,7,8} Number of favourable outcomes = 6 P(E) = 6/8 = 3/4 Hence the probability of arrow...
(iii)Let E be the event of getting a number greater than 5. Outcomes favourable to E is 6. Number of favourable outcomes = 1 P(E) = 1/6 Hence the probability of getting a number greater than 5 is...
Solution: When a die is thrown, the possible outcomes are 1,2,3,4,5,6. Number of possible outcomes = 6 (i) Let E be the event of getting an odd number. Outcomes favourable to E are 1,3,5. Number of...
Solution: Number of blue marbles = 7 Number of white marbles = 8 Number of black marbles = 5 Total number of marbles = 7+8+5 = 20 (i) Probability of getting black , = 5/20 = 1/4 Hence the...
Solution: Number of black balls = 5 Number of red balls = 7 Number of white balls = 3 Total number of balls = 5+7+3 = 15 (i)Probability that the ball drawn is red, = 7/15 (ii) Probability of black...
Solution: Total number of alphabets = 26 Number of vowels = 5 Total number of consonants = 26-5 = 21 Probability that the letter chosen is a consonant , = 21/26 Hence the required probability is...
Solution: Number of defective pens = 12 Number of good pens = 132. Total number of pens = 132+12 = 144 Probability of getting a good pen, P(E) P(E) = 132/144 = 11/12 Hence the required probability...
given table in the question is as follows: Height (in cm) $150–155$ $155–158$ $158–160$ $160–165$ $165–172$ Number of Students $8$ $20$ $25$ $4$ $3$ Solution:- As per the question give we can say...
(ii)
Given table in the question us as follows: Height (in cm) $150–155$ $155–158$ $158–160$ $160–165$ $165–172$ Number of Students $8$ $20$ $25$ $4$ $3$ As per the question give we can say The total...
marks in a unit test.Given table in the question is as follows: Unit Test $I$ $II$ $III$ $IV$ $V$ $VI$ Percentage of marks obtained $72$ $67$ $69$ $74$ $71$ $76$ (iii) The total number of times students get less than...
marks in a unit test. (ii) less than 
marks in a unit test.Given tale in the question is as follows: Unit Test $I$ $II$ $III$ $IV$ $V$ $VI$ Percentage of marks obtained $72$ $67$ $69$ $74$ $71$ $76$ Solution:- According to the question it is given that,...
, what is the probability of losing?As per the question it is given, probability of winning a game is $5/11$ We have to find out the probability of losing, Thus, P(winning)+P(losing) $=1$ Now, P(losing)$=1–$ P(winning) $=1–(5/11)$...
(iii) The probability that taking a yellow ball outside, Number of favorable outcomes $=1$ P(taking a yellow ball outside) = Number of favorable outcomes/total number of Outcomes $=1/3$
We can say by according to the given question, a bag contains 3 balls a red ball, a blue ball and a yellow ball. Now, total number of outcomes $=3$ (i) The probability of taking a red ball outside,...
.(iii) The probability that getting a difference of $1$, Favorable outcomes $=(1,2),(2,1),(2,3),(3,2),(3,4),(4,3),(4,5),(5,4),(5,6),(6,5)$ Number of favorable outcomes $=10$ P(getting a sum of $6$) =...
(ii) two different digitsAs we all know that, A die is rolled one time, the possible outcomes are $1,2,3,4,5$, and $6$. If two dice are rolled then possible outcomes are: $(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)$...
According to the question we can say, a coin is tossed twice. As we all know that, coin has two faces one is head and other one is tail. The possibilities that getting head and tail when three coins...
tailAs per the question it is given that, a coin is tossed twice. As we all know that, coin has two faces one is head and other one is tail. The possibilities of getting head and tail when a coin is...
According to the question it is given that, two coins are tossed together. As we all know that, coin has two faces one is head and other one is tail. The possibilities of getting head and tail when...
playing cards. Find the probability that the card draw is,(v) a face card (vi) a card bearing a number between 
and including both.(v) The probability that getting a face card, In $52$ playing cards there are $12$ face cards, Now, the number of favorable outcomes to the event getting a face card $=12$ Thus, P(card drawn is a...
playing cards. Find the probability that the card draw is,(iii) a king (iv) an ace or a queen(iii) The probability that getting a king, In $52$ playing cards there are $4$ kings, Therefore, the number of favorable outcomes to the event getting a king $=4$ Thus, P(card drawn is a king) =...
playing cards. Find the probability that the card draw is, (i) a diamond (ii) a red cardAccording to the question given, a card is drawn from a pack of well – shuffled $52$ playing cards. (i) The probability that getting a diamond, In $52$ playing cards there are $13$ diamond cards...
, (iv) a number less than 
.(iii) The probability that getting a number divisible by $2$, The number divisible by $2$ in the die $=2,4,6$ Now, the number of favorable outcomes to the event getting a number divisible by $2=3$...
,As we all know that, A die is tossed one time; the possible outcomes are $1,2,3,4,5$, and $6$. Thus, total number of possible outcomes $=6$ (i) The probability of getting an odd number, The odd...
As we all know that, A die is tossed once; the possible outcomes are $1,2,3,4,5$, and $6$. Thus, total number of possible outcomes $=6$ (i) The probability of an even number comes up, The even...
times and frequencies of the outcomes 
were noted as given in the following table. (iii) a number 
Given table in the question is as follows: Outcomes $1$ $2$ $3$ $4$ $5$ $6$ Frequency $73$ $70$ $74$ $75$ $80$ $78$ (iii) Number of times greater than $4$ come up on the die $=80+78=158$ P($>4$...
times and frequencies of the outcomes were noted as given in the following table. (i) (ii) a number 
Given table in the question is as follows: Outcomes $1$ $2$ $3$ $4$ $5$ $6$ Frequency $73$ $70$ $74$ $75$ $80$ $78$ According to the question it is given that,, a die is thrown $450$ times Thus,...
One tail:
No tail: 
Find the probability of occurrence of each of these events.As per the question it is given, Two coins are tossed simultaneously $300$ times, Now, Total number of times 2 tails come up $=83$ P($2$ tails will come up) = Number of times $2$ tails come up/Total...
families with children were selected randomly, and the following data were recorded: (iii) no girlGiven table in the question as follows: Number of girls in a family $0$ $1$ $2$ Number of families $333$ $392$ $275$ (iii) Number of families having no girls $=333$ Now, required probability =...
families with children were selected randomly, and the following data were recorded: (i) girl (ii) girlsGiven table in the question is as follows: Number of girls in a family $0$ $1$ $2$ Number of families $333$ $392$ $275$ According to the question it is given, total number of families $=1000$ (i)...
times and the outcomes were noted as: Head:
, Tail:
. Find the probability of the coin showing up (i) a head, (ii) a tail.According to the question it is given that, A coin is tossed $800$ times, and then total number of trials is $800$. Consider that,${{A}_{1}}$ and ${{A}_{2}}$ be the events of the coin, Then, total...