5. Solve the following regarding probability: 5a.) Let A and B be events in a sa

Question

5. Solve the following regarding probability:

5a.)

Let A and B be events in a sample space S such that P(A) = 0.41, P(B) = 0.46 and P(A B) = 0.14. Find P(A | B).

a) 0.3415

b) 0.0217

c) 0.8913

d) 0.1609

e) 0.3043

f) None of the above.

5b.)

Let A and B be events in a sample space S such that P(A) = 21100 , P(B) = 47100 , and P(A B) = 225 . Find P(B | Ac ).
Hint: Draw a Venn Diagram to find P(Ac B).

a) 0.5949

b) 0.1013

c) 0.8298

d) 2.2381

e) 0.4937

f) None of the above.

5c.)

Suppose that A and B are independent events. If P(A) = 35 and P(B) = 25 , find P(A B).

a) 0.04

b) 1.00

c) 0.24

d) 0.10

e) 0.06

f) None of the above.

5d.)

A pair of fair dice is cast. What is the probabiliy that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even?

a) 0.3667

b) 0.4545

c) 0.3056

d) 0.2778

e) 0.1389

f) None of the above.

Explanation / Answer

5a) P(A | B) =P(AnB)/P(B)=0.14/0.46=0.3043 option e

5b) P(Ac B) =P(B)- P(A B) =47/100-2/25 =39/100

P(Ac)=1-P(A)=1-21/100 =79/100

hence  P(B | Ac ) = P(Ac B)/P(Ac)=(39/100)/(79/100)=39/79=0.4937

option e

5c) P(A B) =P(A)*P(B)=0.24

option C

5d)

probability sum is even =18/36

and number of events where at least one of the numbers falling uppermost is a 1 as well sum is even =5

hence probabiliy that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even =(5/36)/(18/36)=5/18=0.2778

option D

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