Question

1. a survey of students at an art school in kalamazoo, michigan, revealed that 62% prefer classical music when studying rather than no music at all. in addition, 37% of students indicated that they are left - handed. of those surveyed, 14% said they are left - handed and do not prefer classical music.

a. complete the two - way relative frequency table.

	left - handed (l)	not left - handed (~l)	total
do not prefer classical music (~c)	14%
total	37%

b. given that a randomly selected student is not left - handed, what is the probability that they prefer classical music?

Explanation:

Step1: Find left - handed and prefer classical music

We know that the percentage of left - handed students is 37% and the percentage of left - handed students who do not prefer classical music is 14%. So the percentage of left - handed students who prefer classical music is $37\%-14\% = 23\%$.

Step2: Find not left - handed and prefer classical music

The percentage of students who prefer classical music is 62%, and 23% of those who prefer classical music are left - handed. So the percentage of not left - handed students who prefer classical music is $62\%-23\%=39\%$.

Step3: Find not left - handed and do not prefer classical music

The percentage of students who do not prefer classical music is $100\%-62\% = 38\%$. Since 14% of students are left - handed and do not prefer classical music, the percentage of not left - handed students who do not prefer classical music is $38\%-14\% = 24\%$.

Step4: Find the percentage of not left - handed students

The percentage of left - handed students is 37%, so the percentage of not left - handed students is $100\%-37\%=63\%$.

Step5: Find the total percentages

The total percentage of all students is 100%.

The completed two - way relative frequency table:

	Left - handed ($L$)	Not left - handed ($\sim L$)	Total
Do not prefer classical music ($\sim C$)	14%	24%	38%
Total	37%	63%	100%

Step6: Calculate the conditional probability for part b

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, $A$ is the event of preferring classical music and $B$ is the event of being not left - handed.
$P(A\cap B) = 39\%$ and $P(B)=63\%$. So $P(A|B)=\frac{39}{63}=\frac{13}{21}\approx 0.619$ or 61.9%

Answer:

a.

	Left - handed ($L$)	Not left - handed ($\sim L$)	Total
Do not prefer classical music ($\sim C$)	14%	24%	38%
Total	37%	63%	100%

b. $\frac{13}{21}\approx 61.9\%$