Question

Forty percent of world class tennis player are over 6 feet tall. 20 percent of the world class tennis players over 6 feet tall were premature babies. 30 percent of the world class tennis players who are not over 6 feet tall were premature babies. a. Calculate the probability that a randomly selected world class tennis player is over 6 feet tall and was a premature baby. Don't just write a number for the answer. Use the probability notation, simplify the answer, and show your work. b. Calculate the probability that a randomly selected world class tennis player is not over 6 feet tall and was not a premature baby. Don't just write a number for the answer. Use the probability notation, simplify the answer, and show your w ork.

Answer 1

a) There is an 8% probability that a randomly selected world class tennis player is over 6 feet tall and was a premature baby.

b) There is a 42% probability that a randomly selected world class tennis player is not over 6 feet tall and was not a premature baby.

Explanation:

In this problem, we have these following probabilities:

-A 40% probability that a world class tennis player is over 6 feet tall.

-A 60% probability that a world class tennis player is not over 6 feet tall.

-A 20% probability that a world class tennis player over 6 feet tall was a premature baby. This also means that there is a 80% probability that a world class tennis player over 6 feet tall was not a premature baby

-A 30% probability that a world class tennis player who is not over 6 feet tall was a premature baby. This also means that there is a 70% probability that a world class tennis player who is not over 6 feet tall was not a premature baby.

a. Calculate the probability that a randomly selected world class tennis player is over 6 feet tall and was a premature baby.

`P = P_(1)*P_(2)`

`P_(1)` is the probability that a random selected world class tennis player is over 6 feet tall. So

`P_(1) = 0.4`

`P_(2)` is the probability that a world class tennis player over 6 feet tall was a premature baby. So

`P_(2) = 0.2`

`P = P_(1)*P_(2) = 0.4*0.2 = 0.08`

There is an 8% probability that a randomly selected world class tennis player is over 6 feet tall and was a premature baby.

b. Calculate the probability that a randomly selected world class tennis player is not over 6 feet tall and was not a premature baby

`P = P_(1)*P_(2)`

`P_(1)` is the probability that a random selected world class tennis player is not over 6 feet tall. So

`P_(1) = 0.6`

`P_(2)` is the probability that a world class tennis player under 6 feet tall was not a premature baby. So

`P_(2) = 0.7`

`P = P_(1)*P_(2) = 0.6*0.7 = 0.42`

There is a 42% probability that a randomly selected world class tennis player is not over 6 feet tall and was not a premature baby.