## The above frequency distribution table represents the blood groups of 30 students of a class.

[question] Question. The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB. [/question] [solution] Solution: Number of students having blood group AB = 3 Total number of students = 30 Hence, required probability, $\mathrm{P}=\frac{3}{30}=\frac{1}{10}$ [/solution]...

## Eleven bags of wheat flour, each marked 5 kg,

[question] Question. Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg): 4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00 Find the probability that any of these bags chosen at random contains more than 5 kg of flour. [/question] [solution] Solution: Number of total bags = 11 Number of bags containing more than 5 kg of flour = 7 Hence, required probability, $P=\frac{7}{11}$ [/solution]...

## Note the frequency of two-wheelers,

[question] Question. Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, 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. [/question] [solution] Solution: This is an activity based question. Students are advised to perform this activity by yourself. [solution]...

## The distance (in km) of 40 engineers from their residence to their place of work were found as follows.

[question] Question. The distance (in km) of 40 engineers from their residence to their place of work were found as follows. What is the empirical probability that an engineer lives: (i) less than 7 km from her place of work? (ii) more than or equal to 7 km from her place of work? (iii) within $\frac{1}{2} \mathrm{~km}$ from her place of work? [solution] Solution: (i) Total number of engineers = 40 Number of engineers living less than 7 km from their place of work = 9 Hence, required probability...

## To know the opinion of the students about the subject statistics,

[question] Question. 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 (i) likes statistics, (ii) does not like it [/question] [solution] Solution: Total number of students = 135 + 65 = 200 (i) Number of students liking statistics = 135 $\mathrm{P}($ students liking statistics $)=\frac{135}{200}=\frac{27}{40}$ (ii) Number of students who do not...

## An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family.

[question] Question. An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the 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 vehicle. (iii) earning less than Rs 7000 per month and does no...

## Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes

[question] Question. 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. [/question] [solution] Solution: Number of times 2 heads come up = 72 Total number of times the coins were tossed = 200 $P(2$ heads will come up $)=\frac{\text { Number of times } 2 \text { heads come up }}{\text { Total number of times the coins were tossed }}$ $=\frac{72}{200}=...

## In a particular section of Class IX,

[question] Question. In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained: Find the probability that a student of the class was born in August. [/question] [solution] Solution: Number of students born in the month of August = 6 Total number of students = 40 P $($ Students born in the month of August $)=\frac{\text { Number of students born in August }}{\text { Total number of students }}$ $=\frac...

## 1500 families with 2 children were selected randomly,

[question] Question. 1500 families with 2 children were selected randomly, and the following data were recorded: Compute the probability of a family, chosen at random, having (i) 2 girls (ii) 1 girl (iii) No girl Also check whether the sum of these probabilities is 1. [/question] [solution] Solution: Total number of families = 475 + 814 + 211 = 1500 (i) Number of families having 2 girls $=475$ $P_{1}($ a randomly chosen family has 2 girls $)=\frac{\text { Number of families having } 2 \text { gi...

## In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays.

[question] Question. In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. [/question] [solution] Solution: Number of times the batswoman hits a boundary = 6 Total number of balls played = 30 ∴ Number of times that the batswoman does not hit a boundary = 30 − 6 = 24 $P($ she does not hit a boundary $)=\frac{\text { Number of times when she does not hit boundary }}{\text { Total number of balls played }}$ $=\frac{24...