Question

Find the probability of getting the difference of two numbers obtained as a prime number, if a pair of dice are thrown simultaneously.

• A. $\frac{4}{9}$
• B. $\frac{5}{12}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{4}{9}$

Total no. of outcomes = 36
Favourable outcomes =
(1, 3), (1, 4), (1, 6), (2, 4), (2, 5), (3, 1), (3, 5), (3, 6), (4, 1), (4, 2), (4, 6), (5, 2), (5, 3), (6, 1), (6, 3), (6, 4)}

No. of favourable outcomes = 16

For an event
$\text{E, Probability P(E)}$ = $\frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}$

$\therefore$ Probability (difference of two numbers being a prime number) = $\frac{16}{36}=\frac{4}{9}$