Question

fifty - five percent of the members of the junior varsity swim team wear glasses. of the team members 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?
14%
17%
55%
07%

Explanation:

Step1: Calculate the percentage of non - glass - wearers

If 55% of the members wear glasses, then the percentage of members who do not wear glasses is $100\%-55\% = 45\%$.

Step2: Calculate the percentage of 10th - graders among non - glass - wearers

We know that 30% of all members are in the 10th grade. Let's assume the total number of members is 100. There are 55 glass - wearers and 45 non - glass - wearers. We don't know the distribution of 10th - graders between glass - wearers and non - glass - wearers. But we want to find the probability that a randomly chosen member is a non - glass - wearer and in the 10th grade.
We use the formula for conditional probability conceptually. The probability we want is the proportion of non - glass - wearing 10th - graders out of the total number of members.
Let's assume the number of 10th - graders is 30. We don't have enough information to precisely calculate the number of non - glass - wearing 10th - graders in a complex way, but we can make a simple assumption for the sake of this problem.
If we assume the 10th - graders are distributed proportionally among glass - wearers and non - glass - wearers, we first note that the proportion of non - glass - wearers is 45 out of 100.
The probability that a member is a non - glass - wearer and in the 10th grade is calculated as follows:
Let's assume the 10th - graders are split between glass - wearers and non - glass - wearers in the same ratio as the overall team. But a more straightforward way is to think about it in terms of percentages.
The percentage of non - glass - wearers is 45%. We want to find the part of these non - glass - wearers that are 10th - graders.
We know that 30% of all members are 10th - graders.
We assume the distribution is random. The probability $P$ that a member is a non - glass - wearer and in the 10th grade is found by considering the proportion of non - glass - wearers.
If we assume the 10th - graders are distributed randomly among the team, the probability that a member is a non - glass - wearer and in the 10th grade is $P=(1 - 0.55)\times0.30=0.45\times0.30 = 0.135\approx14\%$.

Answer:

14%