Probability Worksheet Solution8





In this page probability worksheet solution8 we are going to see solution of some practice questions of the probability worksheet.

Question 1

If A and B are mutually exclusive events such that P(A) = 3/5 and P(B) = 1/5,then find P (A U B)

Solution:

Since A and B are mutually exclusive events P (A ∩ B) = 0

Addition theorem on probability:

P (A U B) = P(A) + P (B)

P(A) = 3/5    P(B) = 1/5

P (A U B) = (3/5) + (1/5)

             = (3 + 1)/5

             = 4/5


Question 2

If A and B are two events such that P(A) = 1/4,P(B) = 2/5 and P(AUB) = 1/2,then find P(A∩B)

Solution:

P(A) = 1/4

P(B) = 2/5

P(A U B) = 1/2

P(A ∩ B) = P (A) + P (B) - P(A U B)

             = (1/4) + (2/5) - (1/2)

Since the denominators are not same we have to take L.C.M to make them as same

L.C.M = 20

           = (1/4) x (5/5) + (2/5) x (4/4) - (1/2) x (10/10)

           = (5/20) + (8/20) - (10/20) 

           = (5 + 8 -10)/20

           = (13-10)/20

           = 3/20


Question 3

If P(A) = 1/2,P(B) = 7/10,P(AUB) = 1,find

(i) P (A ∩ B)    (ii) P(A' U B')

Solution:

(i) P (A ∩ B)

P (A ∩ B) = P (A) + P (B) - P (A U B)

             = (1/2) + (7/10) - 1

Now we have to take L.C.M to make the denominators as same 

L.C.M = 10

              = (1/2) x (5/5)+ (7/10) - (1/1) x (10/10)

              = (5/10) + (7/10) - (10/10)

              = (5 + 7 - 10)/10

              = (12 - 10)/10

              = 2/10

              = 1/5

(ii) P(A' U B')

 P(A' U B') = P (A ∩ B)'          

               = 1 - P (A ∩ B)

               = 1 - (1/5)

               = (5-1)/5

               = 4/5

probability worksheet solution8 probability worksheet solution8