what is the probability of rolling an even number on the first die and an odd number on the second die…
what is the probability of rolling an even number on the first die and an odd number 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: Probability of even on first die
A die has 6 faces. Even numbers are 2, 4, 6. So the probability of rolling an even number on the first die, $P(A)=\frac{3}{6}=\frac{1}{2}$.
Step2: Probability of odd on second die
Odd numbers on a die are 1, 3, 5. So the probability of rolling an odd number on the second die, $P(B)=\frac{3}{6}=\frac{1}{2}$.
Step3: Use multiplication - rule for independent events
Since the rolls of the two dice are independent events, the probability of both events occurring is $P(A\cap B)=P(A)\times P(B)$. $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.
Answer:
$\frac{1}{4}$