need answers. please show all work. do not post answer in image format. thank yo

Question

need answers. please show all work. do not post answer in image format. thank you

Assume that you have applied to two universities call them A and B) for your degree. In the past, 35% of students with similar credentials as yours who applied to university A were accepted. In the past, 45% of students with similar credentials as yours who applied to university B were accepted. Assume that the applications are independent of each other A) what is the probability that you will be accepted to both of the universities? B) What is the probability that you will be accepted to at least one of the universities?

Explanation / Answer

let

A is event that selected in university A

B is event that selected in university B

A and B are independent

now

given P(A) =0.35 P(B) =0.45

a) we have to find P(A and B )

P(A and B) =P(A) *P(B) (as A and B are Independent)

=0.35*0.45 =0.1575

b)

we have to find P( A or B)

so

P(A or B) =P(A) +P(B) -P(A and B)

=0.35+0.45 -0.1575

=0.80-0.1575 =0.6425

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