Billy Isastar, a famous basketball player, is not a very good free throw shooter. He manages to connect on 65% of his attempts. What is the probability that the first free throw Johnny hits in a game is on his fourth attempt?
a. .015
b. .028
c. .179
d. .096
So he wants
MMMH, where M is miss and H is hit
prob(of your event)
= (.35)^3 (.65) = ....
To find the probability that the first free throw Billy makes in a game is on his fourth attempt, we need to calculate the probability of missing the first three attempts and then making the fourth attempt.
Since Billy connects on 65% of his attempts, his probability of missing an attempt is 1 - 0.65 = 0.35.
The probability of missing the first attempt is 0.35, the second attempt is also 0.35, and the third attempt is also 0.35.
To find the probability of making the fourth attempt, we need to multiply the probabilities of missing the first three attempts by the probability of making the fourth attempt: 0.35 * 0.35 * 0.35 * 0.65 = 0.028.
Therefore, the correct answer is b. .028.
To find the probability that the first free throw Billy hits in a game is on his fourth attempt, we can use the concept of geometric probability.
The probability that Billy misses a free throw is 1 - 0.65 = 0.35, since he connects on 65% of his attempts.
In order for Billy to hit his first free throw on his fourth attempt, he must miss the first three attempts and then hit the fourth attempt. The probability of missing a free throw on a single attempt is 0.35. Since these events are independent, we can multiply the probabilities together:
P(missing on first attempt) * P(missing on second attempt) * P(missing on third attempt) * P(hitting on fourth attempt) = 0.35 * 0.35 * 0.35 * 0.65.
Calculating this expression, we find:
0.35 * 0.35 * 0.35 * 0.65 = 0.042875.
Therefore, the probability that Billy hits his first free throw in a game on his fourth attempt is approximately 0.042875.
Now let's check the answer choices:
a. .015. This is not the correct answer.
b. .028. This is not the correct answer.
c. .179. This is not the correct answer.
d. .096. This is not the correct answer.
None of the given answer choices match our calculations, so the correct answer might not be listed.