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Probability

Short Answer Type

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

1008 Views

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

(0 2 girls (ii) 1 girl (iii) No girl.

Also check whether the sum of these probabilities is 1.

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3. In a particular section of Class IX, 40 students were asked about the months of their birth, the following graph was prepared for the data so obtained. Find the probability that a student of the class was bom in August.

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

Outcome	3 heads	2 heads	1 head	No head
Frequency	23	72	71	28

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

1243 Views

Long Answer Type

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:

Monthly income	Vehicles per family
(in र)	0	1	2	Above 2
Less than 7000	10	160	25	0
7000-10000	0	305	27	2
10000-13000	1	535	29	1
13000–16000	2	469	59	25
16000 or more	1	579	82	88

Suppose a family is chosen. Find the probability that the family chosen is
(i) earning र 10000–13000 per month and owning exactly 2 vehicles.
(ii) earning र 16000 or more per month and owning exactly l vehicle.
(iii) earning less than र 7000 per month and does not own any vehicle.
(iv) earning र 13000–16000 per month and owning more than 2 vehicles.
(v) owning not more than I vehicle.

542 Views

Short Answer Type

Marks (out of 100)	Number of students
0-20	7
20-30	10
30-40	10
40-50	20
50-60	20
60-70	15
70–above	8
Total	90

(i) Find the probability that a student obtained less than 20% in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.

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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

dislike

135

Find the probability that a student chosen at random
(i) likes statistics,
(ii) does not like it.

100 Views

8.
Refer to Q.2, Exercise 14.2. 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 $1 half$ km from her place of work?

Total number of female engineers = 40
(i) Number of female engineers whose distance (in km) from their residence to their place of work is less than 7 km = 9.
∴ Probability that an engineer lives less than 7 km from her plae of work = $9 over 40.$

(ii) Number of female engineers whose distance (in km) from their residence to their place of work is more than or equal to 7 km = 31.

∴Probability that an engineer lives more than or equal to 7 km from her place of residence $equals 31 over 40.$

Aliter: Probability that an engineer lives more than or equal to 7 km from her place of residence = 1 – probability that an engineer lives less than 7 km from her place of work $equals 1 minus 9 over 40 equals 31 over 40$

(iii) Number of female engineers whose distance (in km) from their residence to their place of work is within $1 half space space km space equals space 0 comma$

$therefore$ Probablity that an engineer lives within $1 half space$ km from her place of work = $0 over 40 equals 0.$

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9. Activity: 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.

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10. 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 the 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.

176 Views