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Two dice are thrown simultaneously. The probability that the sum of the numbers appearing on the dice is a prime number is ____.

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Detailed Solution

Two dice are thrown simultaneously. The probability that the sum of the numbers appearing on the dice is a prime number is

512

.
It is given that,

2

dice thrown randomly.
Question Image

The sample space is,

n (S) = 36

.
The combination for the sum of number on

2

dices is prime are,

(1, 1), (1, 2), (2, 1), (2, 3), (3, 2), (4, 1), (1, 4), (1, 6), (6, 1), (2, 5), (5, 2), (4, 3), (3, 4), (5, 6), (6, 5)

.
Let

A

be the event of getting the sum on dice as prime numbers.

n (A) = 15

P (A) = N u m b e r of favourable outcomes T o t a l number of outcomes

The probability for sum of

2

numbers appearing as prime number on two dice is,

= 1536

= 512

Hence, the probability is

512

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