Question

Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team memebers who do not wear glasses, 30 percent of them are in the 10th grade. To the nearest whole percent, what is the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade?.

Answer 1

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

$0.55x$.

The total number of members not wearing glasses, will be

$x - 0.55 x = 0.45 x$.

Now, the no. of members not wearing glasses and in 10th grade will be,

$\frac{0.45x\times30}{100} =0.135x$

We know that the probability of an event E, P(E) will be,

$P(E)=\frac{No.\ of Favourable\ outcomes}{total \ no. \ of \ outcomes}$

So, the probability for no. of members not wearing glasses and in 10th grade will be,

$P(E)=\dfrac{0.135x}{x}$

$P(E)=0.135\\\\P(E)=13.5 \%$

Hence the nearest whole percent of probability is 14%.

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