Question

A quarter back completes 62% of his passes. We want to observe
this quarterback during one game to see how many pass attempts he
makes before completing one pass. What is the probability that the
quarterback throws exactly 4 incomplete passes before he has a
completion? (In other words, his first complete pass occurs on the
5^{th} try).

Answer #1

**Solution:**

Given: A quarter back completes 62% of his passes. That is: p =
probability of success = 0.62

Here X = number of pass attempts he makes before completing one
pass follows geometric distribution with p = 0.62

Thus q = 1 - p = 1 - 0.62 = 0.38

We have to find the probability that the quarterback throws exactly 4 incomplete passes before he has a completion.

The probability mass function of geometric distribution is:

, x = 0,1,2,3,4,.......

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