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

Answer:

The probability of rolling a number less than or equal to 2, then rolling a prime number is $\frac{1}{6}$.

Step-by-step 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

        $=\frac{2}{6}$

        $=\frac{1}{3}$

Compute the value of P (B) as follows:

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

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

        $=\frac{3}{6}$

        $=\frac{1}{2}$

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

$P(A\cap B)=P(A)\times P(B)$

               $=\frac{1}{3}\times \frac{1}{2}$

               $=\frac{1}{6}$

Thus, the probability of rolling a number less than or equal to 2, then rolling a prime number is $\frac{1}{6}$.