Question

Two dice and two coins are tossed. The probability that both the coins show heads and the sum of the numbers found on the dice is a prime number, is

• A. $\frac{5}{72}$
• B. $\frac{1}{12}$
• C. $\frac{13}{144}$
• D. $\frac{5}{48}$

Answer 1

Answer: (D)

$\frac{5}{48}$

Answer 2

The probability that head is shown in one coin is $\frac{1}{2}$ The probability that the sum of the numbers on the dice is a prime = the probability that the following pair of numbers occur on the dice, namely, $(1, 1)$, $(1, 2), (2, 1), (1, 4), (4, 1), (2, 3), (3, 2), (1, 6), (6, 1)$, $(2,5), (5,2),(3,4), (4,3), (6,5), (5,6) =\frac{15}{36}$. $\therefore$ The required probability $=\frac{1}{2}.\frac{1}{2}.\frac{15}{36} = \frac{5}{48}$.