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SBI PO Probability Questions and Answers Quiz 1

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    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 = $P(E)\over P(S)$ = $60\over455$ = $12\over 91$

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