Question

Ellen and Piper take turns shooting free throws. Ellen has probability 0.74 of success and Piper has probability 0.62 of success. If shots are assumed to be independent of each other, what's the probability that Ellen is the first one to make a free throw if she goes first? Give your answer to 4 decimal places.

Answer 1

If Ellen goes first, she will make a free throw with probability 0.74, if she fails the probability is 0.26

Now, its turn of Piper, she will not succeed with probability 0.38

Required probability = 0.74 + 0.26*0.38*0.74 + (0.26*0.38)^2*0.74 + (0.26*0.38)^3*0.74 + ...

The above sequence represents the geometric progression.

a = 0.74
r = 0.26*0.38

using the formula for sum of geometric progression,
sum = a/(1-r)

sum = 0.74/(1 - 0.26*0.38)
sum = 0.8211

Hence required probability = 0.8211