# Probability : Exercise 15.1 (Mathematics NCERT Class 9th)

**Q.1Â Â Â Â Â Â In a cricket match, batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary****.**

**Sol.**

Since in a cricket match ,a batswoman hits a boundary 6 times out of 30 balls she plays i.e., she missed the boundary 30 â€“ 6 = 24 times out of 30 balls.

Therefore, the probability that a batswoman does not hit a boundary.

**Q.2Â Â Â Â Â 1500 families with 2 children were selected randomly, and the following data were recorded : **

** Compute the probability of a family, chosen at random having **

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(i) 2 girlsÂ Â Â Â Â Â (ii) 1 girl Â Â (iii) No girl **

** Also check whether the sum of these probabilities is 1.**

**Sol.**

Let be the event of getting no girl, 1girl and 2 girls.

** (i)** Therefore = Probability of a family having 2 girls

** (ii)** Therefore = Probability of a family having 1 girl

** (iii)** Therefore = Probability of a family having no girls

Therefore Sum of probabilities =

**Q.3Â Â Â Â Â Â Refer to Example 5, section 14.4 Chapter 14. Find the probability that a student of the class was born in August.**

**Sol.**

Clearly from theÂ histograph six students were born in the month of August out of 40 students of a particular section of class - IX.

Probability that a student of the class was born in August

**Q.4Â Â Â Â Â Â Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes : **

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

**Sol.**

Since three coins are tossed 200 times, so the total number of trials is 200.

Probability of getting 2 heads

**Q.5Â Â Â Â Â An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and theÂ number of vehicles in a family.**

** The information gathered is listed in the table below : **

** Suppose a family is chosen. Find the probability that the family chosen is ****(i) earning Rs 10000-13000 per month and owning exactly 2 vehicles. **

** (ii) earning Rs 16000 or more per month and owning exactly 1 vehicles. **

** (iii) earning less than Rs 7000 per month and does not own any vehicle. **

** (iv) earning Rs 13000 -16000 per month and owning more than 2 vehicles. **

** (v) owning not more than 1 vehicle**

**Sol.**

The total number of families = 2400

** (i)** Number of families earning Rs 10000 - 13000 per month and owning exactly 2 vehicles = 29.

Therefore, P (families earning Rs 10000 - 13000 per month and owning exactly 2 vehicles)

** (ii)** Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579.

Therefore P (Families earning Rs 16000 or more per month and owning exactly 1 vehicle)

** (iii)** Number of families earning less than Rs. 7000 per month and does not own any vehicle = 10

Therefore, P (Families earning less than Rs 7000 per month and does not own any vehicle)

** (iv)** Number of families earning Rs 13000 - 16000 per month and owning more than 2 vehicles = 25

Therefore, P (Families earning Rs 13000 - 16000 per month and owning more than two vehicles)

** (v)** Number of families owning not more than 1 vehicle

= Families having no vehicle + Families having 1 vehicle

= (10 + 0 + 1 + 2 + 1) + (160 + 305 + 535 + 469 + 579)

= 14 + 2048 = 2062

P (Families owning not more than 1 vehicle)

**Q.6 Â Â Â Â Â Refer to Table 14.7 Chapter 14. **

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(i) Find the probability that a student obtained less than 20% in the mathematics test. **

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(ii) Find the probability that a student obtained marks 60 or above.**

**Sol.**

Total number of students in mathematics is 90.

** (i)**Â Â Â Clearly, from the given table, the number of student who obtained less than 20% marks in the mathematics test = 7.

P (a student obtaining less than 20% marks) =

** (ii)**Â Â Clearly, from the given table, number of students who obtained marks 60 or above.

= (students in 60 - 70) + (students above 70)

= 15 + 8 = 23

Therefore, P (a student obtaining marks 60 and above) =

**Q.7Â Â Â Â Â To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.**

** Find the probability that a student chosen at random**

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(i) likes statistics, (ii) does not like it.**

**Sol.**

The total number of students = 200

** (i)** P (a student likes statistics)

**(ii)** P (a student does not like statistics)

**Q.8Â Â Â Â Â Refer to Q.2, Ex 14.2. What is the empirical probability that an engineer lives : **

Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(i) less than 7 km from her place of work? **

Â Â Â Â Â Â Â Â Â Â Â Â Â Â **(ii) more than or equal to 7 km from her place of work? **

Â Â Â Â Â Â Â Â Â Â Â Â Â **(iii) within from her place of work?**

**Sol.**

Total number of engineers = 40

** (i)** Number of engineers living less than 7 km from their place of work = 9

Therefore P (an engineer lives less than 7 km from her place of work)

** (ii)** Number of engineers living more than or equal to 7km from her place of work = 31

Therefore P (an engineer lives less than or equal to 7 km from her place of work)

** (iii)** Number of engineer lives within km from her place of work = 0

Therefore P (an engineer lives with km from her place of work) =

**Q.9Â Â Â Â Activity : Note the frequency of two-Â wheeler, three -Â wheelerÂ and four -Â wheelerÂ going past during aÂ timeÂ interval,Â in front of your school gate. **

** Find the probability that any one vehicle out of the total vehicles you have observed is a two wheeler.**

* Sol.Â Â Â Â Â Â *Activity problem : Collect the data and find the desired probability.

**Q.10Â Â Activity : Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that theÂ number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.**

* Sol.Â Â Â Â Â Â *Activity problem : Do as directed and find the desired probability.

**Q.11Â Â Eleven bags of wheat flour, each marked 5 kg , actually contained the following weights of flour (in kg) : **

**Â Â Â Â Â Â 4.97 Â Â Â Â 5.05 Â Â 5.08 Â Â 5.03 Â Â 5.00 Â Â 5.06 Â Â 5.08 Â 4.98 Â 5.04 Â Â 5.07 Â Â 5.00**

** Find the probability that any of these bags chosen at random contains more than 5kg of flour. **

**Sol.**

Total number of wheat bags = 11

Number of bags having more than 5 kg = 7

Therefore P(a bag contains more than 5kg ) =

**Q.12Â Â Â In Q.5 Exercise 14.2 you were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per ****million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 - 0.16 on anyÂ ****of these days.**

**Sol.**

Total number of days = 30

Concentration of sulphur dioxide in 0.12 - 0.16 on any day = 2

ThereforeÂ ,Â Â required probability

**Q.13Â Â Â In Q. 1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding the blood group of 30 students of a class. Use this table to determine the probability that a student of this class,Â selectedÂ at random,Â has blood group AB.**

**Sol.**

Total number of students = 30

Number of students having blood group AB = 3

Therefore Required probability