a six - sided number cube is rolled twice. what is the probability that the first roll is an even number and…

a six - sided number cube is rolled twice. what is the probability that the first roll is an even number and the second roll is a number greater than 4?\n$\frac{1}{6}$\n$\frac{1}{3}$\n$\frac{2}{3}$\n$\frac{5}{6}$

a six - sided number cube is rolled twice. what is the probability that the first roll is an even number and the second roll is a number greater than 4?\n$\frac{1}{6}$\n$\frac{1}{3}$\n$\frac{2}{3}$\n$\frac{5}{6}$

Answer

Explanation:

Step1: Calculate first - roll probability

The even numbers on a six - sided cube are 2, 4, 6. So there are 3 even numbers out of 6. The probability of rolling an even number on the first roll, $P(A)=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate second - roll probability

The numbers greater than 4 on a six - sided cube are 5, 6. So there are 2 numbers greater than 4 out of 6. The probability of rolling a number greater than 4 on the second roll, $P(B)=\frac{2}{6}=\frac{1}{3}$.

Step3: Use multiplication rule for independent events

Since the two rolls are independent events, the probability of both events occurring is $P(A\cap B)=P(A)\times P(B)$. Substitute the values: $P(A\cap B)=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$