 # A local school has both male and female students Each student either plays a sport or doesn't. The two-way table summarizes a random sample of 80 stud usagirl007A 2020-12-24 Answered
A local school has both male and female students Each student either plays a sport or doesnt.
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Step 1
Given,
$\begin{array}{|cccc|}\hline & \text{Female}& \text{male}& \text{Total}\\ \text{No sport}& 12& 15& 27\\ \text{Sport}& 36& 17& 53\\ \text{Total}& 48& 32& 80\\ \hline\end{array}$
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) $\text{P(female)}=\frac{\text{No. of female Students}}{\text{Total number of student}}$
$=\frac{48}{80}$
$=0.6$ $\text{P(Sport and female)}=\frac{\text{No. of students who are female and plays sports}}{\text{Total number of students}}$
$=\frac{36}{80}$
$=0.45$ $\text{P(Sports||female)}=\frac{\text{P(Sports and female)}}{\text{P(female)}}$
$\text{P(Sports||female)}=\frac{\frac{\text{No. of students who are female and plays sports}}{\text{Total number of students}}}{\frac{\text{No. of students who are female}}{\text{Total number of students}}}$
$=\frac{\frac{36}{80}}{\frac{48}{80}}$
$=\frac{0.45}{0.6}$
$=0.75$