Question

At Preston High School, there are two candidates for student body President, Summer and Pedro Based on pre-election polling, it is estimated that 53% of the sophomores plan to vote for Summer, while 52% of the non-sophomores will vote for Pedro. There are 486 students at Preston and 130 of them are sophomores,

a. What is the probability that a randomly selected student will be a sophomore who plans to vote for Summer?

b. Who is expected to win the election

Answer 1

a. Pr(a randomly selected sophomore student who would vote for Summer) = 0.14

b. Pedro would win the election by a margin of 6 votes

Explanation:

Based on the pre-election polling,

Number of students at Preston = 486

Number of sophomore students = 130

Number of non- sophomore students = 486 - 130 = 356

Let us assume that all students of Preston High School will participate in the election.

1. For Summer,

i. 53% of sophomores plan to vote for Summer. So that,

53% of 130 =
`(53)/(100)` × 130

= 68.9

≅ 69

The number of sophomore students that will vote for Summer is 69.

ii. The number of non-sophomores that would vote for Summer = (356 - number of those that would vote for Pedro)

= 356 - 185

= 171

2. For Pedro,

i. The number of sophomore students that would vote for Pedro = (130 - number that would vote for Summer)

= 130 - 69

= 61

ii. 52% of non- sophomores will vote for Pedro. So that;

52% of 356 =
`(52)/(100)` × 356

= 185.12

≅ 185

a. Pr(a randomly selected sophomore student who would vote for Summer)

=
`(69)/(486)`

=
`(23)/(162)`

= 0.14198

≅ 0.14

b. Considering the number of students to vote for each candidate,

Summer = 69 + 171 = 240

Pedro = 61 + 185 = 246

Pedro would be expected to win the election by a margin of 6 votes.