Question

Coach Kennedy will roll a number cube, numbered 1-6, twice. What is the probability of rolling a number less than or equal to 2, then rolling a prime number?

Answer 1

The probability of rolling a number less than or equal to 2, then rolling a prime number is
`(1)/(6)`.

Explanation:

The sample space of rolling a number cube, numbered 1 - 6 is:

S = {1, 2, 3, 4, 5, 6}

The cube is rolled twice.

Denote the events as follows:

A = rolling a number less than or equal to 2 in the first roll

B = rolling a prime number in the second roll

The two events A and B are independent.

This is because the result of rolling the cube the second time will not be dependent on the result of the first roll.

Compute the value of P (A) as follows:

Favorable outcomes = {1, 2} = 2

P (A) = Favorable outcomes of A ÷ Total number of outcomes

`=(2)/(6)`

`=(1)/(3)`

Compute the value of P (B) as follows:

Favorable outcomes = {2, 3, 5} = 3

P (B) = Favorable outcomes of B ÷ Total number of outcomes

`=(3)/(6)`

`=(1)/(2)`

Compute the probability of rolling a number less than or equal to 2, then rolling a prime number as follows:

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

`=(1)/(3)* (1)/(2)`

`=(1)/(6)`

Thus, the probability of rolling a number less than or equal to 2, then rolling a prime number is
`(1)/(6)`.