Question

The table shows the percentage of students in each of three grade levels who list soccer as their favorite sport.

Soccer
Sophomores (35%) 50%
Juniors (33%) 45%
Seniors (32%) 30%
Total (100%) (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 or about 42%
***Find the probability, rounded to the nearest hundredth, that any student selected from all three grades is a junior who lists soccer as the favorite sport

OPTIONS
0.45
0.78
0.15

Answer 1

0.353

Explanation:

We are given the table shows the percentage of students in each of three grade levels who list soccer as their favorite sport.

Sophomores (35%) 50%

Juniors (33%) 45%

Seniors (32%) 30%

Total (100%)= (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 ≈ 42%

Now we are supposed to find the probability, rounded to the nearest hundredth, that any student selected from all three grades is a junior who lists soccer as the favorite sport.

Junior who list soccer as their favorite sport =
`33\% * 45 \% = 0.33 * 0.45=0.1485`

Total students who list soccer as their favorite sport is 42% =0.42

Probability that any student selected from all three grades is a junior who lists soccer as the favorite sport =
`(0.1485)/(0.42)`

=
`0.3535`

Hence the probability, rounded to the nearest hundredth, that any student selected from all three grades is a junior who lists soccer as the favorite sport is 0.353.

Answer 2

35.4%

Explanation:

We are given that,

The percentage of students in junior level who likes soccer = 33% of 45%

i.e. The percentage in junior who likes soccer = = 0.33 × 0.45 = 0.1485 = 14.85%

Also, the total percent of the students who likes soccer = 0.4195 = 41.95% ≅ 42% = 0.42

Thus, we get,

Probability of students in junior level who likes soccer =
`(0.1485)/(0.42)` = 0.354

Thus, the probability of the students in junior level liking soccer is 35.4%