Question

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DETAILS
par
SMITHNM13 13.4.019.
pose a die is rolled twice and let
A = {first toss is a prime} B = {first toss is a 5}
d the requested probability. (Enter the probability as a fraction.)
P(A n B)

Answer 1

The probability of the first toss being a prime and the second toss resulting in a 5 is
`((1)/(12))`.

The requested probability is
`(P(A \cap B))`, where
`(A = {\text{first toss is a prime}})` and
`(B = {\text{second toss is a 5}})`.

To find the probability of the intersection of two events, we can use the formula:

`[P(A \cap B) = P(A) * P(B)]`

The probability of the first toss being a prime is
`((3)/(6))` since there are 3 prime numbers (2, 3, 5) on a standard die, and the die has 6 faces.

The probability of the second toss resulting in a 5 is
`((1)/(6))` since there is 1 face with a 5 out of 6 faces.

Therefore, the probability of both events occurring is:

`[P(A \cap B)` =
`(3)/(6) * (1)/(6) = (1)/(12)]`

So, the probability of the first toss being a prime and the second toss resulting in a 5 is
`((1)/(12))`.

Complete question:

Suppose a die is rolled twice and let

A = {first toss is a prime} C = {second toss is a 5}

Find the requested probability. (Enter the probability as a fraction.) P(A n B)