At the end of regulation time, a basketball team is trailing by one point and a player goes to the line for two free throws. If the player makes exactly one free throw, the goes into overtime. The probability that the first free throw is good is 1/2. However, if the first attempt is good, the player relaxes and the second attempt is good with probability 3/4. However, if the player misses the first attempt, the added pressure reduces the success probability to 1/4. What is the probability that the game goes into overtime?

The probability that the game goes into overtime is 1/4.

Step-by-step explanation:

There are 2 favourable and disjoint events that will led the game into overtime:

1) The first thow goes through and the second one fails

2) The first throw fails but the second one goes through.

We can obtain the probability of going overtime by summing those 2 probabilities.

The probability of failing the second shot after getting a good first shot is 1-3/4 = 1/4. Thus, the probability of event 1 is 1/2 * 1/4 = 1/8.

The probability that the first attemp fails but the second one succeds is 1/2*1/4 = 1/8.

As a consecuence, the probability that the game goes into overtime is 1/8 + 1/8 = 1/4.