Question

you roll a 6 - sided die two times.
what is the probability of rolling a prime number and then rolling a number less than 5?
write your answer as a percentage rounded to the nearest tenth.
%

Explanation:

Step1: Calculate the probability of rolling a prime number

A 6 - sided die has numbers \(1,2,3,4,5,6\). Prime numbers among them are \(2,3,5\). So there are \(3\) prime numbers.
The probability of rolling a prime number \(P(\text{prime})=\frac{3}{6}=\frac{1}{2}\)

Step2: Calculate the probability of rolling a number less than \(5\)

Numbers less than \(5\) on a 6 - sided die are \(1,2,3,4\). So there are \(4\) such numbers.
The probability of rolling a number less than \(5\) \(P(< 5)=\frac{4}{6}=\frac{2}{3}\)

Step3: Use the multiplication rule for independent events

Since the two rolls are independent events, the probability of rolling a prime number and then a number less than \(5\) is \(P = P(\text{prime})\times P(<5)\)
\(P=\frac{1}{2}\times\frac{2}{3}=\frac{1}{3}\)

Step4: Convert the fraction to a percentage

\(\frac{1}{3}\approx0.333\)
To convert to a percentage, multiply by \(100\): \(0.333\times100 = 33.3\%\)

Answer:

\(33.3\%\)