## Probability Worksheet Solution14

In this page probability worksheet solution14 we are going to see solution of some practice questions of the probability worksheet.

Question 14

The probability that a new car will get an award for its design is 0.25,the probability that it will get an award for efficient use of fuel is 0.35 and the probability that it will get both the awards is 0.15. Find the probability that

(i) it will get at least one of the two awards

(ii) it will get only one of the awards

Solution:

Let P (A) be the probability that a new car will get an award for its design

P (A) =  0.25

Let P (B) be the probability that it will get an award for efficient use of fuel

P (B) = 0.35

Let P (A ∩ B) be the probability that it will get both the awards

P (A ∩ B) = 0.15

(i) it will get at least one of the two awards

P (A U B) = P (A) + P (B) - P (A ∩ B)

= 0.25 + 0.35 - 0.15

= 0.45

(ii) it will get only one of the awards

= P (A' ∩ B) + P (A ∩ B')

= P(A) - P (A ∩ B) + P(B) - (A ∩ B)

= (0.25 - 0.15) + (0.35 - 0.15)

= 0.10 + 0.20

= 0.30

Question 15

The probability that A,B and C can solve a problem are 4/5,2/3 and 3/7 respectively.The probability of the problem being solved by A and B is 8/15,B and C is 2/7,A and C is 12/35. The probability of the problem being solved by all the three is 8/35.Find the probability that the problem can be solved by atleast one of them.

Solution:

P (A) = 4/5

P (B) = 2/3

P (C) = 3/7

P (A ∩ B) = 8/15

P (B ∩ C) = 2/7

P (C ∩ A) = 12/35

P(A∩B∩C) = 8/35

P (A U B U C) =  P(A)+P(B)+ P(C)-P(A ∩ B)-P(B ∩ C)-P (C ∩ A)+P(A∩B∩C)

= (4/5)+(2/3)+(3/7)-(8/15)-(2/7)-(12/35)+(8/35)

L.C.M = 105

= (84 + 70 + 45 - 56 - 30 - 36 + 24)/105

= (223 - 122)/105

= 101/105 probability worksheet solution14 probability worksheet solution14