Question

A football quarterback goes for a two-point conversion when the ball is within 10 yards of the end zone. During the game, he has two opportunities for a two-point conversion. He misses the first attempt 50% of the time. When he misses the first attempt, he misses the second attempt 15% of the time. What is the probability of missing both two-point conversion attempts?

Answer 1

Answer:

$P=0.075$,          $P=7.5\%$

Step-by-step explanation:

We look for the probability that the player fails the first attempt and also fails the second attempt.

We know that the probability that the quarterback fails the first attempt is:

$P(1) = 0.5$

We know that the probability that the quarterback fails the second attempt after failing the first is:

$P(2|1) = 0.15$

Then the probability of failure of both attempts is:

$P(2|1)=\frac{P(1\ and\ 2)}{P(1)}$

$P(1\ and\ 2)=P(1)*P(2|1)$

$P(1\ and\ 2)=0.5*0.15$

$P(1\ and\ 2)=0.075$