A pair of fair dice is cast. what is the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one

Question

Vanyuwa [196]

4 years ago

13

A pair of fair dice is cast. what is the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one

of the numbers falling uppermost is a 3?

Mathematics

1 answer:

WITCHER [35] · Answer 1 · 2021-12-31T09:06:17+03:00

If a pair of fair dice is cast, the probability that the <span>sum of the numbers falling uppermost is 9, given that at least one of the numbers falling uppermost is a 3 is given by:

$\frac{P(sum\, of\, 9\, \cup\,3)}{P(3)}$

The number of outcomes of sum of 9 where at last one is 3 is (3, 6) and (6, 3) = 2.

</span>The number of outcomes of last one of the numbers falling uppermost is a 3 is (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (1, 3), (2, 3), (4, 3), (5, 3) and (6, 3) = 11.

Therefore, <span>the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one of the numbers falling uppermost is a 3 is 2 / 11.</span>