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Keisha is playing a game using a wheel divided into 8 equal sectors, as shown in the diagram below. Each time the spinner lands on blue, she will win a prize.
8 section spinner with 1 red, 3 yellow, 3 blue, and 1 green section.
If Keisha spins this wheel twice, what is the probability that she will win a prize on both spins?
Responses
A9/64
B1/4
C1/64
D 3/8
To find the probability that Keisha will win a prize on both spins, we need to first find the probability of her winning on the first spin and then winning on the second spin.
The probability of winning on the first spin is the number of blue sections divided by the total number of sections on the spinner:
P(win on 1st spin) = 3 blue sections / 8 total sections = 3/8
Since Keisha is replacing the prize each time she spins, the probability of winning on the second spin is still 3/8.
To find the probability of winning on both spins, we need to multiply the probabilities of each event happening:
P(win on both spins) = P(win on 1st spin) * P(win on 2nd spin)
P(win on both spins) = (3/8) * (3/8)
P(win on both spins) = 9/64
Therefore, the probability that Keisha will win a prize on both spins is A) 9/64.