Probability Worksheet Solution11





In this page probability worksheet solution11 we are going to see solution of some practice questions of the probability worksheet.

Question 8

A basket contain 20 apples and 10 oranges out of which 5 apples and 3 oranges are rotten. If a person takes out one fruit at random, find the probability that the fruit is either an apple or good fruit.

Solution:

Sample space = 20 apples + 10 oranges

                   = 30 fruits

Number of apples which are rotten = 5

Number of oranges which are rotten = 3

Let A be the event of getting apple

 n (A) = 20

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

       = 20/30

Let B be the event of getting good fruit

 n (B) =Total number of fruits - number of rotten fruits

        = 30 - 8

        = 22

 P (B) = n (B)/n (S)

         = 22/30  

n (A ∩ B) = 15

P (A ∩ B) = n (A ∩ B)/n (S)

              = 15/30

P (A U B) = P (A) + P (B) - P (A ∩ B)

             = (20/30) + (22/30) - (15/30)

             = (20 + 22 - 15)/30

             = (42 - 15)/30

             = 27/30

             = 9/10

P (A U B) = 9/10


Question 9

In a class,40% of the students participated in mathematics quiz,30% in science quiz and 10% in both the quiz programmes. If a student is selected at random from the class,find the probability that the student participated in mathematics or science or both quiz programmes.

Solution:

Total number of students = 100

                          n (S) = 100

Let A be the event that the student participated in mathematics quiz

 n (A) = 40

 P (A) = n (A)/n (S)

         = 40/100

Let B be the event that the student participated in science quiz

 n (B) = 30

 P (B) = n (B)/n (s)

        = 30/100

(A ∩ B) be the event that the student participated in both quiz

 n (A ∩ B) = 10

P (A ∩ B) = n (A ∩ B)/n (S)

             = 10/100

P (A U B) = P (A) + P (B) - P (A ∩ B)

              = (40/100) + (30/100) - (10/100)

              = (40 + 30 - 10)/100

              = 60/100

              = 6/10

P (A U B) = 3/5

probability worksheet solution11 probability worksheet solution11