what is the probability of rolling an odd number on the first die and an even number on the second die…
what is the probability of rolling an odd number on the first die and an even 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
Answer:
$\frac{1}{4}$
Explanation:
Step1: Probability of odd on first die
A die has 6 faces numbered 1 - 6. Odd numbers are 1, 3, 5. So probability $P(O_1)=\frac{3}{6}=\frac{1}{2}$.
Step2: Probability of even on second die
Even numbers on a die are 2, 4, 6. So probability $P(E_2)=\frac{3}{6}=\frac{1}{2}$.
Step3: Use multiplication rule for independent events
Since the rolls of the two dice are independent events, the probability of both events occurring is $P = P(O_1)\times P(E_2)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.