Question

11.2: probability
score: 11/16 answered: 7/10
question 6
a die is rolled twice. what is the probability of showing a 5 on the first roll and an even number on the second roll?
your answer is :
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Explanation:

Step1: Calculate the probability of getting a 5 on the first roll

A die has 6 faces. The probability of rolling a 5 on the first roll is $P(5)=\frac{1}{6}$.

Step2: Calculate the probability of getting an even number on the second roll

The even numbers on a die are 2, 4, 6. So there are 3 even numbers. The probability of rolling an even number on the second roll is $P(\text{even})=\frac{3}{6}=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the two rolls are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P(5)\times P(\text{even})=\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$