If you spin the spinner below twice, what is P(vowel, then P)?
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
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.
To find the probability of spinning a vowel, then spinning a P, we need to determine the probability of each event separately and then multiply them together.
There are a total of 6 sectors on the spinner, and 2 of them are vowels (I and O). Therefore, the probability of spinning a vowel on the first spin is 2/6 = 1/3.
After the first spin, the spinner is not reset, so there are now 5 sectors left. Since there is only 1 sector labeled P, the probability of spinning a P on the second spin is 1/5.
To find the overall probability, we multiply the individual probabilities together:
P(vowel, then P) = (1/3) * (1/5) = 1/15
So the answer is B. One-ninth.