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

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

Step-by-step 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 = × 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 = × 356  

                                              = 185.12

                                              ≅ 185

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

                                             =

                                             =

                                             = 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.

step-by-step explanation: