Type of Graphs, Charts with Worked Problems

Question 20

Question:   A die is thrown 50 times. 26 times the number which was shown on the top face was even. If the die is thrown again, what is the probability of getting an odd number?

Answer:    Total number of trials =50

Number of times an even number was got = 26

Number of times an odd number was got= 24

P(getting an odd number)

Question 21

Question:   The runs scored by a cricketer in six innings are given below:

What is the probability that he would score a half-century in an innings?

Answer:    Number of times he has scored an half-century = 4

P(his scoring a half century)

Question 22

Question:   750 families with 2 children were selected randomly, and the following data were recorded:


Compute the probability of a family chosen at random, having i) no by ii) 1 boy iii) 2 boys. Also check whether the sum of these probabilities is 1.

Answer:    E₁ : the family has no boy

E₂ : the family has one boy

E₃ : the family has two boys

Question 23

Question:   A bag contains red, blue and green balls. One ball is drawn at random from this bag, its colour is noted and then the ball is put back into the bag. This is repeated 125 times and the observations are recorded as follows:



What is the probability that the ball drawn is not blue?

Answer:   

Question 24

Question:   A person fires 50 times at a target and hits the target 30 times. When he fires the next time at the target. What is the probability that he hits the target?

Answer:    The probability of hitting the target

Question 25

Question:   A dice is thrown 500 times and the frequencies of the outcomes and noted as follows:

When the dice is thrown again what is the probability of a prime number showing up?

Answer:    Total number of trials = 500

Number of trials in which a prime number showed up = 48 + 82 + 96

= 226

P(getting a prime number)

Question 26

Question:   In the EXIT POLL results given by a TV Channel in the past few years, it was observed that 65 out of 80 times, the predictions proved correct. What is the probability that the next EXIT POLL result given by the TV channel will be correct? What is the probability that the result will be in correct?

Answer:    E : The exit poll result is correct

Total number of trials = 80

Number of times the result is correct = 5



Probability of the result being incorrect

Question 27

Question:   A survey was conducted about the distance travelled each day by the employees of a company to their place of work and the result is given below:



If an employee is chosen at random, what is the probability
1) that he travels less than 10 KM?
2) that he travels 20 km or more?
3) that he travels less than 20 km but not less than 10 km? Is the sum of these probabilities equal to one?

Answer:    E₁ : the employee travels less than 10 KM

E₂: the employee travels 20 km or more but not less than 10 km

Total number of trials = 30 + 172 + 180 + 58 + 35 + 25 = 500

Number of trials in which the outcomes is E₁
= 30 + 172 = 202




Number of trials in which the outcome is E₂
= 35 + 25 = 60




Number of trials in which the outcome is E₃
= 180 + 58 = 238



P(E₁) + P(E₂) + P(E₃) = 0.404 + 0.12 + 0.476

Question 28

Question:   The marks of a student in 10 tests are given below:


If 60% and above is I class, what is the probability that the student gets I class in any test?

Answer:    Total number of tests = 10

Number of tests in which the student gets I class = 6

Probability of getting I class

Question 29

Question:   A study was conducted on a group of 1000 people (randomly selected) in a city to find a relation between age and the number of visits to a hospital in a year. The data obtained is in the following table.

If a person chosen at random from the city, find the probability of his
1) being between 10 and 30 years and visiting and visiting the hospital thrice in the year
2) being below 60 years and visiting the hospital twice.
3) visiting the hospital only once
4) being between 30 and 60 years of age and visiting the hospital more than twice

Answer:   
1) Total number of people = 1000

Number of people who are between 10 and 30 years of age whose number of visits to the hospital is 3 = 57.

P(the person is between 10 and 30 years of age and whose Number of visits to the hospital is 3)


2) Number of people below 60 years visiting the hospital twice

=26 + 60 + 36 =122


P(the person is below 60 years and visits the hospital twice)



3) Number of people who visit the hospital only once

= 16 + 86 + 52 + 12 = 166

P (the person visits the hospital only once)


4) Number of people between 30 - 60 years visiting the hospital more than twice

= 64 + 50 + 50 = 164

P (the person is between 30 - 60 years and visits the hospital more than twice)