the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade is 14%.
Given, the members of the junior varsity swim team wear glasses is 55%.
And the members of junior varsity swim team who do not wear glasses and in 10th grade is 30%.
Let the total no. of members be x.
So, the members of the junior varsity swim team wear glasses (55%),will be
.
The total number of members not wearing glasses, will be
.
Now, the no. of members not wearing glasses and in 10th grade will be,
![\frac{0.45x\times30}{100} =0.135x](https://tex.z-dn.net/?f=%5Cfrac%7B0.45x%5Ctimes30%7D%7B100%7D%20%3D0.135x)
We know that the probability of an event E, P(E) will be,
![P(E)=\frac{No.\ of Favourable\ outcomes}{total \ no. \ of \ outcomes}](https://tex.z-dn.net/?f=P%28E%29%3D%5Cfrac%7BNo.%5C%20of%20Favourable%5C%20outcomes%7D%7Btotal%20%5C%20no.%20%5C%20of%20%5C%20outcomes%7D)
So, the probability for no. of members not wearing glasses and in 10th grade will be,
![P(E)=\dfrac{0.135x}{x}](https://tex.z-dn.net/?f=P%28E%29%3D%5Cdfrac%7B0.135x%7D%7Bx%7D)
![P(E)=0.135\\\\P(E)=13.5 \%](https://tex.z-dn.net/?f=P%28E%29%3D0.135%5C%5C%5C%5CP%28E%29%3D13.5%20%5C%25)
Hence the nearest whole percent of probability is 14%.
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