Respuesta :
(A) bb and ss are not mutually exclusive because P(B∩S)=5/78.
Given total students = 78
students in band = 35
students in sports = 32
students not in band Or sports = 16
total students in band, in sports, not in both = 35 + 32 + 16 = 83
the students which are in both band and sports = 83 - 78 = 5
We know that,
P(B) = probability of selecting a student which in band
P(S) = probability of selecting a student which in sports
P(B∩S) = P(B) * P(S)
P(B∩S) = 5/78
So there are 5 students who are both in the band and in a sports team. The events can occur at the same time, they are not mutually exclusive.
So (A) is the right answer bb and ss can not be mutually exclusive since P(B∩S)=5/78
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The full question is :
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 bb represent the event of selecting a student in the band, and let event ss represent the event of selecting a student on a sports team. Are bb and ss mutually exclusive events?
A) No, because P(B∩S)=5/78
B) No, because P(B∩S)=48/78
C) No, because P(B∩S)=62/78
D) Yes, because P(B∩S)=5/78
E) Yes, because P(B∩S)=62/78
