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consider selecting a student Consider selecting a student randomly at a certain

ID: 3205350 • Letter: C

Question

consider selecting a student Consider selecting a student randomly at a certain university, suppose the probability that the student is math major is 0.2, and the probability that suppose student is a biology major is 0.4. of the students major both math and biology. What is the probability that the selected student is either a math major or biology major? What is the probability that the selected student is of some other major? What is the probability that the selected student is not a double major (math and biology)? If a student is selected is a math major, what is the probability that he is not a biology major? Suppose you select two students randomly from this university, what is the probability that both of them are math majors?

Explanation / Answer

Let,

Event A: Seleted student is a Math major

Event B: Seleted student is a Biology major

By the given information we have;

P(A) = 0.2 ; P(B) = 0.4 and P(AB) = 0.06

a. Prob that selected student is a Math or Biology major = P(AB)

= P(A) + P(B) - P(AB)

= 0.2 + 0.4 - 0.06

= 0.54

b. Prob that selected studen is of another major = Prob that student is neither a Maths major nor a Biology major

= P(AB)c

= 1- P(AB)

= 1- 0.54

= 0.44

c. Prob that the selected student is not a double major = 1 - (Prob of being a double major)

= 1- P(AB)

= 1 - 0.06

= 0.94

d. Prob that a student is not a biology major given that the student is a Maths major = P(Bc|A)

= P(BcA) / P(Bc)

Numerator = P(BcA)

= P(A) - P(AB) )

= 0.2 -0.06

= 0.14

Denominator =   P(Bc)

= 1 - P(B)

= 1 - 0.4

=0.6

Thus Prob that a student is not a biology major given that the student is a Maths major =  0.14 / 0.6

= 0.2333

e. Prob that two selected students are math major = 0.2 x 0.2

= 0.04