Question

According to a recent? study, 8.6?% of high school dropouts are? 16- to? 17-year-olds. In? addition, 5.7?% of high school dropouts are white? 16- to? 17-year-olds. What is the probability that a randomly selected dropout is? white, given that he or she is 16 to 17 years? old? The probability that a randomly selected dropout is? white, given that he or she is 16 to 17 years? old, is nothing. ?(Round to four decimal places as? needed.)

Answer 1

Answer: the probability that a randomly selected dropout is white is 0.4902%

Explanation:

According to the provided information,

8.6% of high school dropouts are in the age bracket of 16 to 17 years old.

Then 5.7% of the high school dropouts that are 16 to 17 years old are whites.

Therefore, the probability that a randomly selected dropout is white =

5.7% of 8.6% = 0.4902%.

For clarity sake, we can assume that there are 3000 students in the high school.

8.6% are dropouts :

8.6/100 × 3000 = 258 total dropouts.

Now, suppose 5.7% of the total dropouts in that school are whites, therefore the number of white dropouts in the school is:

5.7/100 × 258

= 14 white dropouts.

We can also achieve this by multiplying the two percentages by the total number of students in the school

i.e 8.6% × 5.7% × 3000

= 14 whites dropouts

This affirms that the probability that a randomly selected dropout is white =

5.7% × 8.6% = 0.4902%

Answer 2

0.6628 or 66.28%

Explanation:

The probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old is determined by the probability of them being a white 16 to 17 years old dropout (5.7%), divided by the probability of them being a 16 to 17 years old dropout of any ethnicity (8.6%):

`P(W|16\ to\ 17)=(P(W\ and\ 16\ to\ 17))/(P(16\ to\ 17)) =(0.057)/(0.086)\\P(W|16\ to\ 17)=0.6628=66.28\%`

There is a 0.6628 or 66.28% chance that a randomly selected dropout is white, given that he or she is 16 to 17 years old.