Thread: Probability

Please show any working out. Any help will be apprciated.
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My tennis coach analyses every game that I play. She has found that I get the first serve in about 70% of the time. When I get the first serve in, I win the point about 80% of the time. If I miss the first serve, the second serve goes in about 90% of the time. When this happens, I win the point about 30% of the time.
a) Find the probability that I win a point when I am serving
b) If I win a point while serving, what is the probability that I only
needed one serve?

Originally Posted by Joker37

Please show any working out. Any help will be apprciated.

__________________________________________________ __________________________________________________ __
My tennis coach analyses every game that I play. She has found that I get the first serve in about 70% of the time. When I get the first serve in, I win the point about 80% of the time. If I miss the first serve, the second serve goes in about 90% of the time. When this happens, I win the point about 30% of the time.
a) Find the probability that I win a point when I am serving
b) If I win a point while serving, what is the probability that I only
needed one serve?

I suggest you draw a tree diagram. Do this and it should be clear where the following have come from:

a) (0.7)(0.8) + (0.3)(0.9)(0.3) = ....

b) Pr(First serve in | win the point while serving) = (0.7)(0.8)/[(0.7)(0.8) + (0.3)(0.9)(0.3)] = ....