Answered: Assume that 69.3% of the student…

Name: Assume that 69.3% of the student athletes are male, 49.7% of the stude
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Description: Assume that 69.3% of the student athletes are male, 49.7% of the student athletes prefer basketball, 32.3% prefer football, and the rest prefer track. Zero female athletes prefer football. If a randomly selected student athlete prefers basketball, wh

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that 69.3% of the student athletes are male, 49.7% of the student athletes prefer basketball, 32.3% prefer football, and the rest prefer track. Zero female athletes prefer football. If a randomly selected student athlete prefers basketball, what is the probability that the student athlete is female?

Expert Solution

Step 1

Assume,

M be the event that the selected student is a man.
W be the event that the selected student is a woman.
B be the event that the selected student prefers basketball.
F be the event that the selected student prefers football.
T be the event that the selected student prefers track.
The total number of athletes is 100.

The required probability is conditional probability that the selected student is a woman given that the selected student prefers basketball. It can be written as, $P (\frac{W}{B})$ .

By using the conditional probability formula, $P (\frac{W}{B})$ can be given as, $P (\frac{W}{B}) = \frac{P (W \cap B)}{P (B)}$ .

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