Question

A high school science teacher has 78 students. Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let event B represent the event of selecting a student in the band, and let event S represent the event of selecting a student on a sports team. Are B and S mutually exclusive events?

Answer 1

Answer:

Explanation: no because intersection of b and s is equal to 5/78.

Answer 2

Two events are said to be mutually exclusive, if the two events cannot occur simultaneously, hence the intersection of such event defined as (BnS) will be 0. However, since P(BnS) ≠ 0 ; then both events are not mutually exclusive.

We can obtain the probability of (BnS) as follows :

n(BnS) = number of students who are both in the band and in the sport team.

Let, this portion of students be represented as x :

(35-x) + (32-x) + x + 16 = 78

35 - x + 32 - x + x + 16 = 78

83 - x = 78

83 - 78 = x

5 = x

Hence, n(BnS) = 5

Therefore, the probability of B and S will be :

• n(BnS) / total number of students
• P(BnS) = 5/78

Since, P(BnS) ≠ 0 ; then the events are not mutually exclusive

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