Question

you spin the spinner twice. what is the probability of landing on an even number and then landing on an odd number? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Count total and even numbers

The spinner has 6 numbers. Even - numbered outcomes are 4, 6, 8, so there are 3 even - numbered outcomes. The probability of landing on an even number on the first spin, $P(E_1)=\frac{3}{6}=\frac{1}{2}$.

Step2: Count odd numbers

Odd - numbered outcomes are 3, 5, 7, so there are 3 odd - numbered outcomes. The probability of landing on an odd number on the second spin, $P(O_2)=\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the two spins are independent events, the probability of landing on an even number first and then an odd number is $P = P(E_1)\times P(O_2)$. Substitute the values: $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$