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.

Question

13-09-2019
Mathematics

contestada

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.

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joaobezerra joaobezerra · Answer 1 · 2019-09-20T21:07:32+02:00

Answer:

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.

Step-by-step 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.

[tex]P = P_{1}*P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that a random selected world class tennis player is over 6 feet tall. So

[tex]P_{1} = 0.4[/tex]

[tex]P_{2}[/tex] is the probability that a world class tennis player over 6 feet tall was a premature baby. So

[tex]P_{2} = 0.2[/tex]

[tex]P = P_{1}*P_{2} = 0.4*0.2 = 0.08[/tex]

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

[tex]P = P_{1}*P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that a random selected world class tennis player is not over 6 feet tall. So

[tex]P_{1} = 0.6[/tex]

[tex]P_{2}[/tex] is the probability that a world class tennis player under 6 feet tall was not a premature baby. So

[tex]P_{2} = 0.7[/tex]

[tex]P = P_{1}*P_{2} = 0.6*0.7 = 0.42[/tex]

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.