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