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

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• 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}

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