suppose you spin the spinner twice. what is the probability of spinning a red, then green? p(red, green) =…
suppose you spin the spinner twice. what is the probability of spinning a red, then green? p(red, green) = ? show your answer as a fraction in lowest terms. enter the numerator.
Answer
Explanation:
Step1: Determine probability of spinning red
The spinner is divided into 8 equal - sized sections, and 3 of them are red. So the probability of spinning a red on the first spin, $P(\text{red})=\frac{3}{8}$.
Step2: Determine probability of spinning green
After the first spin, the situation for the second spin is the same (since spins are independent events). There are 2 green sections out of 8. So the probability of spinning a green on the second spin, $P(\text{green})=\frac{2}{8}=\frac{1}{4}$.
Step3: Calculate the combined probability
Since the two spins are independent events, we use the multiplication rule for independent events: $P(A\text{ and }B)=P(A)\times P(B)$. Here, $A$ is spinning a red and $B$ is spinning a green. So $P(\text{red, green})=\frac{3}{8}\times\frac{1}{4}=\frac{3}{32}$.
Answer:
3