Question

Two dice are thrown simultaneously. Find the probability of getting prime number on each die.

Answer 1

Given: Two fair six-sided dice are thrown simultaneously; find P(prime on each die).

Step-wise calculation:

1. Total outcomes = 6 × 6 = 36.

2. Prime faces on a die = {2, 3, 5} so 3 favorable faces; P(prime on one die) = `3/6` = `1/2`.

3. For two independent dice, favourable ordered outcomes = 3 × 3 = 9.

So, P(both prime) = `9/36`

= `1/4` 

Equivalently P = `1/2 xx 1/2`

= `1/4`

The probability that each die shows a prime number = `1/4` (0.25).