Question

you roll a 6 - sided die two times.
what is the probability of rolling a divisor of 45 and then rolling a number greater than 3?
write your answer as a decimal.

Explanation:

Step1: Find the probability of rolling a divisor of 45

The divisors of 45 within 1 - 6 are 1, 3, 5. So there are 3 favorable outcomes.
The probability \(P_1=\frac{3}{6}=\frac{1}{2}\)

Step2: Find the probability of rolling a number greater than 3

Numbers greater than 3 on a 6 - sided die are 4, 5, 6. So there are 3 favorable outcomes.
The probability \(P_2=\frac{3}{6}=\frac{1}{2}\)

Step3: Use the multiplication rule for independent events

Since the two rolls are independent events, the probability \(P = P_1\times P_2\)
\(P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}= 0.25\)

Answer:

\(0.25\)