Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together.


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1 Required Probability = where Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together. Solution: As girls are always together so they are considered as a group. So there are 7 things to be arranged (6 boys, group of girls). They can be arranged in ways. Now internal arrangement of girls can be done in ways. Favorable ways = ways Total ways = ways Required probability Q2) What is the probability that a card drawn at random from a pack of 52 cards is either a king or a spade? Bank Clerk 2010, PO 2014 Solution: There are 13 spades and 3 other kings. So, required probability is Q3) A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least 1 women? Bank PO 2008, 2011, 2015 Solution: = Q4) A basket contains 3 blue and 4 red balls. If 3 balls are drawn at random from the basket, what is the probability that all the three balls are either blue or red? Bank PO 2010, 2017 Solution: Ways of getting blue balls = Ways of getting red balls = Q5) An urn contains 3 red and 4 green marbles. If 3 marbles are picked at random, what is the probability that 2 are green and 1 is red? New India Insurance 2009 Solution: Number of ways of selecting 3 marbles out of 7 marbles = Ways of selecting 2 green and 1 red marble = 1
2 Directions for Q6Q9 Study the information given below and answer the questions that A basket contains 4 red, 5 blue and 3 green marbles. Bank PO 2010, 2012 Q6) If 2 marbles are drawn randomly, then what is the probability that both are blue? Solution: Q7) If 3 marbles are drawn at random, then what is the probability that at least one is blue? Placement Papers Ways of selecting 3 marbles such that none is blue = = Q8) If 3 marbles are picked at random, then what is the probability that all are of the same color? Bank PO 2014, 2015 Ways of selecting 3 marbles of same color = Q9) If 3 marbles are picked at random, then what is the probability that exactly two are of the same color? Bank PO 2010, 2012 Ways of selecting 3 marbles such that exactly 2 are of same color = Directions for Q10: Study the information given below and answer the questions that 2
3 A basket contains 3 blue, 5 red and 2 green balls. Bank PO 2007, 2011, 2015 Q10) If 4 balls are picked at random, then what is the probability that two are blue and two are green? Solution: Favorable cases = Total cases = Directions for Q11: Study the information given below and answer the questions that A basket contains 4 red, 6 blue, 3 yellow and 2 green marbles. Bank PO 2010 Q11) If 4 marbles are picked at random, what is the probability that two are red, one is yellow and one is green? Solution: Ways of selecting 4 marbles = Ways of selecting 2 red marbles = Ways of selecting a yellow marble = Ways of selecting a green marble = Q12) A die is thrown twice. What is the probability of getting a 4 or 5 on the first throw and a 2 or 3 on the second throw? Placement Papers Solution: Probability of getting a 4 or 5 on the first throw = Probability of getting a 2 or 3 on the second throw = Q13) A speaks truth in 75% cases and B in 80%. In what percentage of cases are they likely to contradict each other when describing the same event? Placement Paper 1) 35% 2) 30% 3) 25% 4) 20% Solution: or 35% 3
4 Directions for Q14Q15: Study the information given below and answer the questions that A bag contains 4 white and 2 black balls. Another contains 3 white and 5 black balls. If one ball is drawn from each bag, find the probability that Q14) Both are white? Solution: Probability of getting white ball from bag 1: Probability of getting white ball from bag 2: Q15) One is white and one is black? Solution: P(Black from 1st and white from 2nd) + P(White from 1st and black from 2nd) Q16) A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn in red. Solution: Select Bag 1 and get a red ball + Select Bag 2 and get a red ball = Q17) What is the probability that birthday of 12 people will fall in 12 different calendar months (Assuming equal probabilities for 12 months). Solution: Total number of cases = Favorable Cases = Q18) Three persons A, B and C throw a dice in succession till one gets a six and wine the game. Find the probability of A winning, if A begins. Solution: A can win the game if he gets a six in the 1st, 4th, 7th throw. P(A) =, = A will get fourth throw if he fails in the first, B fails in the second, C fails in the third. Probability of A winning in the fourth throw = Similarly, Probability of A winning in the seventh throw = 4
5 Probability of A winning = 5
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