Probability Worksheet Solution9





In this page probability worksheet solution9 we are going to see solution of some practice questions of the probability worksheet.

Question 4

If a die is rolled twice,find the probability of getting an even number in the first time or a total of 8.

Solution:

Sample space = {(1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6)

                       (2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6)

                       (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6)

                       (4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6)

                       (5,1) , (5,2) , (5,3) , (5,4) , (5,5) , (5,6)

                       (6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6)}    

Let A be the event of getting even number in the first time

A = {(2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) 

       (4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6)

       (6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6)}

 n (A) = 18

P (A) = n (A)/n (S)

        = 18/36

Let B be the event of getting a total of 8

B = {(2,6), (3,5), (4,4), (5,3), (6,2)}

n (B) = 5

P (B) = n (B)/n (S)

        = 5/36

A ∩ B = {(2,6), (4,4), (6,2)}

 n (A ∩ B) = 3

P (A ∩ B) = n (A ∩ B)/n (S)

             = 3/36

P (A U B) = P (A) + P (B) - P (A ∩ B)

             = (18/36) + (5/36) - (3/36)

             = (18 + 5 - 3)/36

             = (23 - 3)/36

             = 20/36

             = 10/18

  P (A U B) = 5/9


Question 5

One number is chosen randomly from the integers 1 to 50. Find the probability that it is divisible by 4 or 6.

Solution:

Sample space (S) = {1,2,3,4,5,6,7,8,............................50}

                n (S) = 50

Let A be the event of getting a number which is divisible by 4

A = {4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , 36 , 40 , 44 , 48}

 n (A) = 12

Probability of getting a number which is divisible by 4, P (A) = n (A)/n (S)

                                                                                = 12/50

Let B be the event of getting a number which is divisible by 6

B = {6 ,12 , 18 , 24 , 30 , 36 , 42 , 48}

 n (B) = 8

Probability of getting a number which is divisible by 6, P (B) = n (B)/n (S)

                                                                                = 8/50

A ∩ B = {12 , 24 ,36 , 48}

 n (A ∩ B) = 4

 P (A ∩ B) = n (A ∩ B)/n (S)

              = 4/50

P (A U B) = P (A) + P (B) - P (A ∩ B)

             = (12/50) + (8/50) - (4/50)

             = (12 + 8 - 4)/50

             = (20 - 4) /50

             = 16/50

             = 8/25

P (A U B) = 8/25

probability worksheet solution9 probability worksheet solution9