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Two dice are thrown. What is the probability that the sum of numbers on two dice are 9 or numbers on two dice are prime numbers?

Two dice are thrown. What is the probability that the sum of numbers on two dice are 9 or numbers on two dice are prime numbers? Correct Answer 13/36

Given:

Two dice are rolled then,

Number of outcomes = 36

Calculation:

Outcomes when sum of numbers on two dice is 9 =

= {(3,6), (4, 5), (5, 4), (6, 3)}

= 4

Probability when sum of numbers is 9 = 4/36 = 1/9

Outcomes when two numbers are prime =

= {(2,2), (2,3) (2,5), (3,2), (3,3), (3,5), (5,2), (5,3), (5,5)}

= 9

Probability that two numbers are prime numbers =

= 9/36 = ¼

Required probability = 1/9 + ¼ = 13/36

Tricks:

Maximum sum of numbers on two dice = 12

Total number of prime numbers in a die = (2, 3 and 5) = 3

Total outcomes that two numbers are prime numbers = 3 × 3 = 9

Required probability = 9/36 = 1/4

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