Probability Distributions Question about Freethrows

Question

Bob has a 98% chance of making any freethrow. He throws until he misses. Determine the chance that:

a) he misses for the first time on the 9th or 10th throw

b) he misses for the first time on the 5th throw

c) What is the expected number of shots before a miss?

Am I supposed to use the hypergeometric distribution for this question? Because you can classify failures and successes... How would I go about solving this? Thank you.

Answer 1

Just use the geometric distribution. Hints for a and b: b) If you miss for the first time on the fifth shot. What does that mean for the first four shots? a) You should ask your self the same question as in b. Afterwards you only have to add up the probabilities.

Think about what it means to miss in the context of the geometric distribution. http://en.wikipedia.org/wiki/Geometric_distribution

Now for c) you only need to calculate the expected value for $\text{Geo}(\lambda)$. What is $\lambda$ in this context?.

Answer 2

Solutions for a and b:

b) Prob. of missing on the 5th throw for the first time is $0.98^4\cdot (0.02)$ --- he doesn't miss 4 times, then he misses. (Of course, I assume independence which is not entirely plausible).

a) On the 9th or 10th throw. For the ninth: $p_9=0.98^8(0.02)$, for the tenth: $p_{10}=0.98^9(0.02)$ then $p_9+p_{10}$ is what you're looking for.