TS EAMCET · Maths · Probability
In a game, two dice are thrown simultaneously by a person \(\mathrm{A}\) and two cards are drawn at random simultaneously from a pack of 52 playing cards by a person B. They win the game if A gets a prime score as the sum of the numbers appear on both the dice and \(B\) gets a face card and a card having a prime number. Then the probability. that both \(\mathrm{A}\) and \(\mathrm{B}\) win is
- A \(\frac{8}{663}\)
- B \(\frac{40}{663}\)
- C \(\frac{16}{117}\)
- D \(\frac{40}{221}\)
Answer & Solution
Correct Answer
(B) \(\frac{40}{663}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {} P(A \text { and } B \text { win })=P(A \text { win }) \times P(B \text { win }) \\ & =\frac{15}{36} \times \frac{{ }^{12} C_1 \times{ }^{16} C_1}{{ }^{52} C_2}=\frac{5}{12} \times \frac{12 \times 16}{26 \times 51}=\frac{40}{663} .\end{aligned}\)
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