Solved: "A local school has both male and female..."

usagirl007A

Answered question

2020-12-24

A local school has both male and female students Each student either plays a sport or doesnt.

Answer & Explanation

Elberte

Skilled2020-12-25Added 95 answers

Step 1
Given,

\begin{array}{cccc} Female & male & Total \\ No sport & 12 & 15 & 27 \\ Sport & 36 & 17 & 53 \\ Total & 48 & 32 & 80 \end{array}

Let Sports be the event that a randomly chosen student plays a sport.
Let Female be the event that a randomly chosen student is a female.
Step 2
The required probabilities are obtained as follows- a)

P(female) = \frac{No. of female Students}{Total number of student}

= \frac{48}{80}

= 0.6

P(Sport and female) = \frac{No. of students who are female and plays sports}{Total number of students}

= \frac{36}{80}

= 0.45

P(Sports||female) = \frac{P(Sports and female)}{P(female)}

P(Sports||female) = \frac{\frac{No. of students who are female and plays sports}{Total number of students}}{\frac{No. of students who are female}{Total number of students}}

= \frac{\frac{36}{80}}{\frac{48}{80}}

= \frac{0.45}{0.6}

= 0.75

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