# Free throw Probability [duplicate]

Suppose a basketball player has an 80 percent chance of making a free throw. He has been fouled, and has two free throws. If a free throw is made, its counts as one point. Let $X$ and $Y$ be the number of points from the first and second free throw respectively. Figure out the joint probabilities for $X$ and $Y$, the expected number of points from the two free throws, and the variance for this number of points, when:

a) each free throw is an independent event

b) $P(Y=1\mid X=1)=0.9$ and $P(Y=1\mid X=0)=0.4$ so that making the first free throw raises the probability of making the second free throw.

So I've pretty much done part a but the only thing I'm confused about is when I find the expected number of points from the two free throws its less than 1. Should it be that way? Than, for part b it only gives me two of the probabilities and I'm a little confused about how to find the other two. I tried setting it up into a two by two box with X values on top and Y values on the side but still couldn't figure that out. Any input would be appreciated. Thanks!

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## marked as duplicate by apnorton, AlexR, amWhy, 1999, RecklessReckonerJul 17 '14 at 17:40

$$\text {with} \space P(Y=1\mid X=1)=0.9 \space \text{you can find}\space P(Y=0 \mid X=1) = 0.1$$ $$\text {with} \space P(Y=1\mid X=)=0.9 \space \text{you can find}\space P(Y=0 \mid X=1) = 0.1$$