## write about probability. Collect the data related to your family members month wise and tabulate them. also calculate the probabil

Question

write about probability. Collect the data related to your family members month wise and tabulate them. also calculate the probabilities month wise.

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3 months 2021-07-21T01:07:52+00:00 2 Answers 0 views 0

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. … The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Sol. Here, the total number of trials = 30

Number of times the ball touched boundary = 6

Number of times, the ball missed the boundary = 30 � 6 = 24

Let the event not hitting the boundary be represented by E, then

Thus, the required probability = 0.8

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

Number of girls in a family 2 1 0

Number of families 475 814 211

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 I.

Sol: Total number of families = 1500.

(i) Number of families having 2 girls in a family = 475

Probability of family having 2 girls in a family

(ii) Number of families having 1 girl = 814

Probability of family having 1 girl in a family

(iii) Number of families having no girl in a family = 211

Probability of a family having no girl in a family

Now, the sum of the obtained probabilities

i.e., Sum of the above probabilities is 1.

3. Refer to Question 5, Section 14.4, Chapter 14 of NCERT Textbook. Find the probability that a student of the class was born in August.

Sol. From the graph, we have:

Total number of students born in various months in a year = 40

Number of students born in August = 6

Probability of a student of the IX-Class who was born in August

4. Three coins are tossed simultaneously 200 times with the following frequencies of derent outcomes:

Frequency 23 72 77 28

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

Sol. Total number of times the three coins are tossed = 200

Number of outcomes in which 2 heads coming up = 72

Probability of 2 heads coming up

Thus, the required probability

If the three coins are simultaneously tossed again, then the probability is 25

5. An organisation 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 pmbability that the family chosen is

(i) earning 10000-13000 per month and owning exactly 2 vehicles.

(ii) earning f 16000 or more per month and owning exactly 1 vehicle.

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

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

(v) owning not more than 1 vehicle.

Sol. Here, total number of families = 2400

(i) Number of families having earning Rs. 10000 � Rs. 13000 per month and 2 vehicles = 29

Probability of a family (having earning Rs. 10000 � 13000 and 2 vehicles)

(ii) Number of families having earning Rs. 16000 or above and owning 1 vehicle = 579

Probability of a family (having earning Rs. 16000 and above and 1 vehicle)

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

Probability of a family (having earning less than Rs. 7000 and owning no vehicle)

(iv) Number of families having earning Rs. 13000 �16000 and owing more than 2 vehicles = 25

Probability of a family (having earning Rs. 13000 � 10000 and owning no vehicle)

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

= [Number of families having no vehicle] + [Number of families having only 1 vehicle]

=[10 + 1 + 2 + 1] + [160 + 305 + 535 + 469 + 579]

= 14 + 2148

= 2162

Probability of a family (owning not more than one vehicle)

6. Refer to Table 14.7, Chapter 14 of NCERT Textbook.

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

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

Sol. From the table 14.7, we have:

Marks Number of students

0-20 7

20-30 10

300 10

40-50 20

50-60 20

60-70 15

70 and above 8

Total 90

Total number of students = 90

(i) From the given table number of students who have obtained less than 20% marks = 7

Probability of a student (obtaining less than 20% marks)

(ii) From the given table, number of students who obtained marks 60% or above

= [Number of students in class-interval 60-70] + [Number of students in the class interval 70 and above]

= 15 + 8 = 23

Probability of a student (who obtained 60 marks and above)

7. 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.

Opinion Number of students

, actually contained the following weights of flour (in kg):

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