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Probability Questions Answers

  • 15. Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that ball is white

    1. 1
    2. 2/3
    3. 1/3
    4. 4/3
    Answer And Explanation

    Answer: Option B

    Explanation:

    Total cases = 10 + 20 = 30
    Favourable cases = 20

    So probability = 20/30 = 2/3

  • 16. There is a pack of 52 cards and Rohan draws two cards together, what is the probability that one is spade and one is heart ?

    1. 11/102
    2. 13/102
    3. 11/104
    4. 11/102
    Answer And Explanation

    Answer: Option B

    Explanation:

    Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

    Let sample space be S
    \begin{aligned}
    \text{then, n(S) = }^{52} C _2 \\
    => \frac{52 \times 51}{ 2 \times 1} = 1326 \\
    \text {let E be event of getting 1 spade and 1 heart} \\
    \text{So, n(E) = ways of getting 1 spade or 1 heart out of 13} \\
    = ^{13}C_1 \times ^{13}C_1 \\
    = 13 \times 13 \\
    = 169 \\
    \text{So, p(E) = }\frac{n(E)}{n(S)} \\
    = \frac{169}{1326} = \frac{13}{102}
    \end{aligned}