Correct Answer - Option 2 : 91/216
Given:
Three dice are thrown simultaneously.
Concepts used:
A fair die is numbered from 1 to 6 with probability of coming of each number being 1/6.
Total number of outcomes on roll of three dice = 216
Calculation:
Even prime numbers out of 1 to 6 is 2.
⇒ Probability of getting number of outcomes in which even prime number appears on at least one die = P (Number of outcomes in which 2 appears on one die + Number of outcomes in which 2 appears on two dice + Number of outcomes in which 2 appears on three dice)
⇒ P (Number of outcomes in which even prime number appears on at least one die) = P {(3 × 1/6 × 5/6 × 5/6)} + P {(3 × 1/6 × 1/6 × 5/6)} + P {(1/6 × 1/6 × 1/6)} = 91/216
∴ Probability of getting a number on at least one die equal to even prime number is 91/216.
Alternative solution:
The only even prime number out of 6 numbers (1, 2, 3, 4, 5, 6) is 2.
⇒ P (2 comes on at least one die) = 1 - P (2 comes on neither die)
⇒ P (2 comes up on at least one die) = 1 - (5/6 × 5/6 × 5/6)
⇒ P (2 comes up on at least one die) = 91/216.
∴ Probability of getting a number on at least one die equal to even prime number is 91/216.
