2) Two unbiased coins are tossed. What is the probability of obtaining tail in both the coins ? 1/4
3) An unbiased die is rolled
A) What is the probability of getting 5 ?
B) What is the probability of getting an even number?
C) What is the probability of getting a number greater than 3? 1/6,1/2,1/2
4) Two unbiased dice are thrown together. Find the probability of obtaining
A) 5 in both the dice. 1/36
B) 3 in 1 and 4 in the other. 1/18
C) same number in both the dice. 1/6
5) A card is drawn at random from a pack of 52 cards. Find the probability of obtaining
A) a black card. 1/2
B) a diamond. 1/4
C) an Ace. 1/13
6) A card is drawn at random from a pack of 52 cards. what is the probability
A) the card is king. 1/13
B) the card is not king ? 12/13
7) An urn contains 5 red and 4 white balls. 3 balls are drawn at random from the urn. What is the probability that all the balls are red ? 5/42
8) A leap year is selected random. What is the probability that it will content 53 Mondays ? 2/7
9) A box contains 3 white and 5 black balls. A ball is drawn at a random.
A) What is the probability that the ball is black ?
B) find the odds in favour of the events
C) odd in against. 5/8, 5:3,3:5
10) A card is drawn at random from a pack of 52 cards. Find the probability that the card is a spade or an Ace? 4/13
11) Two unbiased dice are thrown.
A) What is the probability that the sum of the digits on the dice is 7. 1/6
B) Find also the odds in favour of this event. 1:5
22) 8 men in a company of 25 are graduates. If three men are selected from 25 men at random, What is the probability that
A) they are all graduates. 14/575
B) at least one of them is graduate. 81/115
23) There are 4 white and 3 black balls in a bag. If four balls are drawn at random then what is the probability that 2 of them are white and two or black ? 18/35
24) three unbiased coins are and tossed. What is the probability that all of them are heads. 1/8
25) A card is drawn at random pack of 52 cards. What is the probability that
A) the card is not a club. 3/4, 1/2
B) the card is neither a spade no a heart.
26) Two unbiased dice are rolled. What is the probability that the product of the digits in the dice is 12. 1/9
27) In a family there are two childrens. Find the probability they will have different birthdays. 364/365
28) A pair of dice is thrown. Find the probability that the sum of the two numbers is neither 8 nor 10. 7/9
29) A box contains 6 green balls and 4 yellow balls. 3 balls are drawn from the box at random. What is the probability that out of 3 balls 2 are green and one is yellow. 1/2
30) 4 unbiased dies are thrown at random. Find the probability of getting different digits in the four dice. 5/18
31) 6 unbiased coins are tossed together. What is the probability
A) exactly 4 heads. 15/64
B) at least 4 heads. 11/32
32) 5 unbiased coins are tossed together. Find the probability of obtaining 3 heads & 2 tails. 5/14
33) 3 unbiased coins are tossed together. Find the sample space in connection with it. Find the probability
A) at least one head. 7/8
B) exactly one tail. 3/8
34) 10 balls are distributed at random in 3 boxes. What is the probability of keeping 3 balls in the first box. 5120/19683
35) If 20 dates are named to random. What is the probability that 5 of them will be Mondays ? 15505 x6¹⁵/7²⁰
36) Two unbiased dies are thrown. Find the probability that the sun of the faces equals or exceeds 10. 1/6
37) If for the two events A and B, P(A)= 3/8 , P(B)=5/8 and P(A U B)=3/4. Then find the values of
A) P(A/B). 2/5
B) P(B/A). 2/3
Also examine whether A and B are independent or not.
38) There are two identical urns. One of them contains 4 white and 3 red balls and the other contains 3 white and 7 red balls. An urn is choosen at a random and a ball is drawn from it. Find the probability that the ball is white. If the ball is white then find the probability that it is taken from the first urn. 61/140, 40/61
39) if A and B are two independent events and P(A)=1/5, P(B)=2/3 then find the value of P(A U B). 11/15
40) if A and B are two events such that P(A)= 1/3 , P(B)=1/4 and P(A UB)=1/2 then find the value of
A) P(A ∩B'). 1/4
B) P(A/B'). 1/3
41) If two events are mutually independent then prove that their complementary events are also mutually independent.
42) There are 4 white, 3 red and 3 blue balls in a box and 5 white, 4 red and 3 blue balls in another box. If a ball is drawn at random from each of the boxes then find the probability that both of them are the same colour. 41/120
43) There are 3 red and 4 white balls in a bag. Two balls are drawn at random one after another, without replacement.
A) what is the probability that the ball drawn in the second time is white ?
B) under the condition that the second ball is white, what is the probability that the first ball is white ? 4/7, 1/2
44) A and B are two events such that P(A UB)= 7/8, P(A ∩B) = 1/4, P(B) =1/4. Find
A) P(A) . 3/8
B) P(B). 3/4
C) P(A ∩B'). 1/8
45) A box contains 4 red and 3 blue balls. Two balls are drawn at a time twice from that box. Find the probability that the first two balls are red and the next two balls are blue when first two balls are
A) replaced. 2/49
B) not replace before drawing the next two. 3/35
46) The first bag contains 5 white and 4 Black balls. The second Back contains 3 white and seven black balls. A ball is drawn at random from the first bag and is kept in a second bag. Now a ball is drawn at random from the second bag. What is the probability that a ball is white ? 32/99
47) if P(A) = 2/3 , P(B) = 1/2 and P(A UB) = 1 then find the value of
A)P(A/B). 1/3
B) P(A/B'). 1
C) P(A' ∩B'). 0
Are the events A and B mutually exclusive ? No
48) Suppose that all the four possible outcomes e₁ e₂ , e₃ and e₄ of an experiment are equally likely. If A={e₁,e₂}, B{e₂ , e₃}, C= e₃,e₄} then prove that A and B are independent, B and C are independent but A and C are not independent.
49) In an examination 30% students failed in mathematics, 20% students failed in chemistry and 10% students failed in both mathematics and Chemistry. A student is selected at random. What is the probability that
A) the student may fall in mathematics if it is known that the student has failed in chemistry. 1/2
B) the student may fail in mathematics or chemistry ? 2/5
50) The chance of solving a problem by 3 students are 2/7, 3/8 and 1/2 respectively. If each of them try independently. Find the chance that the problem is solved. 87/112
51) if A and B be two independent events and P(A)=2/3, P(B) =3/5 then find the values of
A) P(AU ∩B). 2/5
B) P(A∩B). 13/15
52) A candidate is selected for interview for 3 posts. For the first post there are three candidates, for the second post there are 4 candidates and for the third post there are two candidates. What is the chance of his getting at least one post ? 3/4
53) There are three identical boxes containing red and blue balls. In the first box there are 3 red and 2 blue balls, in the second there are 4 red and 5 blue balls and in the third there are two red and 4 blue balls. A box is chosen at random and a ball is drawn from it. If the ball is drawn be red then What is the probability that it has been drawn from the second box ? 10/31
54) an integer is choose at random from the first 200 positive integers. find the probability that chosen integer is divisible by 6 or 8. 1/4
55) The probability of winning of a player is 3/10 if the path of the running is fast, and the probability of winning is 2/5. if the path is slow. At a particular day the probability that path is fast is 7/10 and the probability that the path is slow Is 3/10. Find the probability of winning of that player on that day. 33/100
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