Question

section 5.3 homework score: 6/13 answered: 6/13 question 7 a die is rolled twice. what is the probability of getting a 1 on the first roll and an even number on the second roll? round to four decimal places. your answer is :

Explanation:

Step1: Probability of getting 1 on first roll

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

Step2: Probability of getting an even number on second roll

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

Step3: Use the multiplication rule for independent events

Since the two rolls of the die are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P(1)\times P(\text{even})$.
$P=\frac{1}{6}\times\frac{1}{2}=\frac{1}{12}\approx0.0833$

Answer:

0.0833