SOLVING WORD PROBLEMS ON PROBABILITY

Problem 1 :

The record of a weather station shows that out of the past 150 consecutive days, its weather forecasts were correct 110 times.

i) What is the probability that it was correct on a given day ?

ii) What is the probability that it was not correct on a given day ?

Solution :

Records taken for 150 consecutive days = 150

Its weather forecasts were correct 110 times.

i) The forecast was correct on a given day

= 110/150

Ii) The forecast was not correct on a given day

= 150 – 110

= 40

= 40/150

= 4/15

Problem 2 :

The percentage of marks obtained by a student in the monthly unit tests are given below :

Based on this data, find the probability that the students gets more than 75% marks in a unit test.

Solution :

Total number of unit test = 6

Percentage of marks obtained in more than 75 is 3.

= 3/6

= 1/2

Problem 3 :

A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information so obtained is listed in the following table :

i) Of a household earning $10000 – $14999 per year and having exactly one television.

ii) Of a household earning $25000 more per year and owning two television.

iii) Of a household not having any television.

Solution :

The total number of the households = 4000

i) Number of household earning $10000 – $14999 per year and having exactly one television = 240

Required probability = 240/4000

= 3/50

ii) Number of household earning $25000 more per year and owning two television = 760

Required probability = 760/4000

iii) Number of a household not having any television = 30

Required probability = 30/4000

= 3/400

Problem 4 :

Two dice are thrown simultaneously 500 times. Each time the sum of the two numbers appearing on their tops is noted and recorded as given in the following table :

If the dice are thrown once more, what is the probability of getting the sum :

i) 3 ?

ii) More than 10 ?

iii) Less than or equal to 5 ?

iv) Between 8 and 12 ?

Solution :

Total trials = 500

i)

= 3/500

Probability of getting the sum as 3 = 30/500

= 3/50

ii) To find the sum more than 10 :

= (28 + 15)

= 43

 = 43/500

iii)To find the sum less than or equal to 5 :

= (14 + 30 + 42 + 55)

= 141

Probability = 141/500

iv) To find between 8 and 12 :

= (53 + 46 + 28)

= 127

Probability = 127/500

Problem 5 :

Over the past 200 working days, the number of defective parts produced by a machine is given in the following table :

Determine the probability that tomorrow’s output will have :

i) No defective part.

ii) At least one defective part.

iii) Not more than 5 defective parts.

iv) More than 13 defective parts.

Solution :

Total days = 200

i) No defective part = 50

Probability of no defective parts = 50/200

= 1/4

ii) At least one defective part = 200 – 50

= 150

The probability that tomorrow’s output will have = 150/200

= 3/4

iii) Not more than 5 defective parts

= 50 + 32 + 22 + 18 + 12

= 146

The probability that tomorrow’s output will have = 146/200

= 73/100

iv) More than 13 defective parts = 0

Problem 6 :

A school management committee interviewed some people for the post of principle. The committee wanted that the female candidate should also be given the fair chance. So, they called the male & female candidates 2 : 3 ratio.

i) What is the probability that female candidate being selected ?

Solution :

The male & female candidates 2 : 3 ratio.

i) The probability that female candidate being selected

= 3/(2 + 3)

= 3/5

Problem 7 :

100 cards marked from 2 to 101 are placed in a box & mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card is :

i) An even number.

ii) A number, which is a perfect square ?

iii) A prime number less than 20.

Solution :

Total cards = 100

Sample space n(s) = 100

i) Even number = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100}

Total even number = 50

The probability that number on the even number card is : 50/100

= 1/2

ii) Perfect square = (4, 9, 16, 25, 36, 49,  64, 81, 100)

= 9/100

iii) Prime number less than 20 is :

= (2, 4, 6, 8, 10, 12, 14, 16, 18, 20)

= 10/100

= 2/25

Problem 8 :

A survey was conducted in a group of students as a part of their environment awareness program in which they collected the following data regarding the number of plants planted in 30 hours in a locality

i) Find the probability of the number of hours having 12 – 15 plants.

ii) Find the probability of number of hours having less than 6 plants.

Solution :

Total hours = 30

i) The probability of the number of

hours having 12 – 15 plants = Number of hours/total hours

= 8/30

= 4/15

ii) The probability of number of hours = 9/30

having less than 6 plants

= 3/10