what is the probability of rolling an odd number on the first die and a four on the second die? write your…

what is the probability of rolling an odd number on the first die and a four on the second die? write your answer as a fraction or a whole number. with fractions, use a slash ( / ) to separate the numerator and denominator.

what is the probability of rolling an odd number on the first die and a four on the second die? write your answer as a fraction or a whole number. with fractions, use a slash ( / ) to separate the numerator and denominator.

Answer

Explanation:

Step1: Calculate probability of first - die event

A die has 6 faces numbered from 1 to 6. The odd - numbered faces are 1, 3, 5. So the probability of rolling an odd number on the first die, $P(A)=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate probability of second - die event

The probability of rolling a 4 on the second die. Since there is 1 face with the number 4 out of 6 faces, $P(B)=\frac{1}{6}$.

Step3: Use the multiplication rule for independent events

Since the rolls of the two dice are independent events, the probability of both events occurring is $P(A\cap B)=P(A)\times P(B)$. Substitute $P(A)=\frac{1}{2}$ and $P(B)=\frac{1}{6}$ into the formula: $P(A\cap B)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$