SBI PO Probability Questions and Answers Quiz 1

1 . Directions (1 - 5): Study the given information carefully to answer the questions that follow. An urn contains4 green, 5 blue 2 red and 3 yellow marbles. $Q.$ If two marbles are drawn at random, what is the probability that both are red or at least one is red ? A.   $26\over93$ B.   $2\over7$ C.   $199\over366$ D.   None of these 2 . If three marbles are drawn at random, what is the probability that at least one is yellow? A.   $1\over 5$ B.   $199\over 364$ C.   $135\over 324$ D.   $5\over 9$ 3 . If eight marbles are drawn at random, what is the probability that there are equal number of marbles of each colour? A.   $3\over 8$ B.   $351\over 738$ C.   $60\over 1001$ D.   $1\over 1011$ 4 . If three marbles are drawn at random, what is the probability that none is green ? A.   $3\over 8$ B.   $273\over 748$ C.   $30\over 91$ D.   None of these 5 . A bag contains 13 white and 7 black balls. Two balls are drawn at random. What is the propability that they are of the same of the colour? A.   $41\over 190$ B.   $21\over 190$ C.   $59\over 190$ D.   $99\over 190$ 6 . From a well - shuffled pack of 52 playing cards. one card is drawn at random. What is the probabilty that the card drawn will be a black king ? A.   $1\over 26$ B.   $7\over 13$ C.   $3\over 13$ D.   $9\over 13$ 7 . Directions (7-10): Study the given information carefully and answer the questions that follow : An urn contains 3 red, 6 blue, 2 green & 4 yellow marbales . $Q.$ If two marbles are picked at random, what is the probability that one is green, two are blue and one is red? A.   $4\over 15$ B.   $17\over 280$ C.   $6\over 91$ D.   $11\over 15$ 8 . If two marbles are picked at random, what is the probability that eigher both are red or both are green ? A.   $3\over 5$ B.   $4\over 105$ C.   $2\over 7$ D.   None of these 9 . If four marbles are picked at random, what is the probability that at least one is yellow ? A.   $91\over 123$ B.   $69\over 91$ C.   $125\over 143$ D.   $1\over4$ 10 . If three marbles are picked at random, what is the probability that two are blue and one is yellow ? A.   $2\over 15$ B.   $6\over 91$ C.   $12\over 91$ D.   $3\over 15$

Answers & Solutions   1 .     Answer : Option D Explanation : Total number of marbles in the urn = 4 + 5 + 2 + 3 = 14 Total possible outcomes = selection of 2 marbles out of 14 marbles = 14$C_2$ = $14\times13\over 1\times2$ = 91 Favourable number of cases = 2$C_2$ + 2$C_1$ x 12$C_1$ = 1 + 2 x 12 = 25 Required probability = $25\over 91$ 2 .     Answer : Option B Explanation : Total possible outcomes = 14$C_3$ = $14\times13\times12\over1\times2\times3$ = 364 (When no marble in yellow), Favourable no.of cases = 11$C_3$ = $11\times10\times9\over1\times2\times3$ = 165 Probability that no marble is Yellow = $165\over 364$ Required Probaility = 1 - $165\over 364$ = $364 - 165 \over 364$ = $199 \over 364$ 3 .     Answer : Option C Explanation : Total possible outcomes = 14$C_8$ = 14$C_6$ = $14\times13\times12\times11\times10\times9\over1\times2\times3\times4\times5\times6$ = 3003 Favourable no.of cases = 4$C_2$ x 5$C_2$ x 2$C_2$ x 3$C_2$ = 6 x 10 x 1 x 3 = 180 Required probability = $180\over 3003$ = $60\over 1001$ 4 .     Answer : Option C Explanation : Total possible outcomes = 14$C_3$ = $14\times13\times12\over1\times2\times3$ = 364 No ball is green, Total favourable outcomes = selection of 3 marble out 5 blue, 2 red and 3 yellow marbles = 10$C_3$ = $10\times9\times8\over1\times2\times3$ = 120 Required probability = $120\over 364$ = $30\over 91$ 5 .     Answer : Option D Explanation : Total possible outcomes = 20$C_2$ = $20 \times 19\over 1\times 2$ = 190 Total favourable outcomes = 13$C_2$ x 7$C_2$ = $13 \times 12\over 1\times 2$ + $7 \times 6\over 1\times 2$ = 78 + 21 = 99 Required probability = $99\over 190$ 6 .     Answer : Option A Explanation : Total possible outcomes = 52 $C_ 1$ = 52 Favourable outcomes = 2 Required probability = $2\over 52$ = $1\over 26$ 7 .     Answer : Option C Explanation : P(S) = 15$C_4$ P(E) = 2$C_1$ x 6$C_2$ x 3$C_1$ = 2 x 15 x 3 = 90 Required probability = $P(E)\over P(S)$ = $90\over 1365$ = $6\over 91$ 8 .     Answer : Option B Explanation : P(S) = 15$C_2$ = 105 P(E) = 3$C_2$ = 2$C_2$ = $3\times 2\over 1\times 2$ + 1 = 4 Required probability = $4\over 105$ 9 .     Answer : Option B Explanation : P(S) = 15$C_4$ = $15\times14\times13\times12\over 1\times2\times3\times4$ = 1365 Let no yellow marble is selected. P(E) = Selection of 4 marbles out of 11 marbles = 11$C_4$ = $11\times10\times9\times8\over 1\times2\times3\times4$ = 330 Reqruied probability = 1 - $330\over 1365$ = 1 - $22\over 91$ = $91 - 22\over 91$ = $69\over 91$ 10 .     Answer : Option C Explanation : P(S) = 15$C_3$ = $15\times 14\times 13\over 1 \times 2 \times 3$ = 455 P(E) = selection of 2 marbles out of 6 blue marble and that of one marble out of 4 yellow marbles = 6$C_2$ x 4$C_1$ = $6\times 5\over 1\times 2$ x 4 = 60 Required probability = $P(E)\over P(S)$ = $60\over455$ = $12\over 91$