If you spin the spinner below twice, what is P(vowel, then P)?

Question

A spinner is divided evenly into 6 sectors. From the top of the spinner clockwise, the sectors are labeled I, O, E, N, P, and U. The spinner arrow points to the sector labeled P.
A. one-third
B. one-ninth
C. start fraction 5 over 6 end fraction
D. Start fraction 5 over 12 End fraction

Answer 1

Since there are six equally likely sectors that the spinner can land on, the probability of landing on any one sector is 1/6.

For the first spin, we want to know the probability of landing on a vowel (I, O, E, or U), which is 4 out of 6 possible sectors. So the probability of spinning a vowel on the first spin is 4/6, or 2/3.

Now, for the second spin, we want to know the probability of landing on the sector labeled P, which is 1 out of 6 possible sectors.

To find the probability of both events happening (spinning a vowel first, then spinning P), we multiply the probabilities:

P(vowel, then P) = P(vowel) x P(P)

P(vowel, then P) = (4/6) x (1/6)

P(vowel, then P) = 4/36

Simplifying, we get:

P(vowel, then P) = 1/9

Therefore, the answer is (B) one-ninth.