Q78 / 160 · TS EAMCET 2023 (13 May Shift 2) · Mathematics

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
    $\frac{8}{663}$
  • Correct answer
    B
    $\frac{40}{663}$
  • C
    $\frac{16}{117}$
  • D
    $\frac{40}{221}$

Solution

$\begin{aligned} & \text {} P(A \text { and } B \text { win })=P(A \text { win }) \times P(B \text { win }) \\ & =\frac{15}{36} \times \frac{{ }^{12} C_1 \times{ }^{16} C_1}{{ }^{52} C_2}=\frac{5}{12} \times \frac{12 \times 16}{26 \times 51}=\frac{40}{663} .\end{aligned}$

Hence, the correct answer is option: 'B'.

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