Question

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

• A. $\frac{1}{36}$
• B. $0$
• C. $\frac{1}{3}$
• D. $\frac{1}{12}$

Answer 1

The correct option is A $\frac{1}{36}$

Sample space when pair of die are thrown,

$S=\left\{\begin{array}{c}(1,1)(1,2)(1,3)(1,4)(1,5),(1,6),\\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6)\\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\end{array}\right\}$

$n\left(S\right)=36$

Let $E$ be the favourable event of gettng even prime number on both die

$E=(2,2)$

Probability of getting even prime number on both die

$P\left(E\right)=\frac{1}{36}$

$\therefore$ Probability of obtaining an even prime number on each die $=\frac{1}{36}$