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

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- History of statistics.
- Branches of statistics.
- Uses of statistics.
- Collection of statistical data
- classification of data
- Tabulation of data
- Construction of statistical table
- Arithmetic mean
- Geometric mean
- Harmonic mean
- Median
- Mode
- Quartiles