Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number.

Given: Two dice are thrown at the same time and the product of numbers appearing on them is noted.

To do: To find the probability that the product is a prime number.

Solution:

Total no. of possible outcomes$=6^2=36$

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

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

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

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

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

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

Out of these, product of outcomes that would be prime would be

$( 1,\ 2),\ ( 1,\ 3),\ ( 1,\ 5),\ ( 2,\ 1),\ ( 3,\ 1),\ ( 5,\ 1)$.

Probability $=\frac{No.\ of\ favorable\ outcomes}{Total\ possible\ outcomes}=\frac{6}{36}=\frac{1}{6}$

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Updated on: 10-Oct-2022

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