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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.

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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

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

Also check whether the sum of these probabilities is 1.

Total number of families
= 475 + 814 + 211 = 1500
(i) Probability of a family, chosen at random,

having 2 girls = $475 over 1500 equals 19 over 60$

(ii) Probability of a family, chosen at random,

having 1 girl $equals 814 over 1500 equals 407 over 750$

(iii) Probability of a family, chosen at random,

having no girl $equals 211 over 1500$

Sum of these probabilities

$equals 19 over 60 plus 407 over 750 plus 211 over 1500 equals fraction numerator 475 plus 814 plus 211 over denominator 1500 end fraction equals 1500 over 1500 equals 1$

Hence, the sum is checked.

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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.

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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

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?

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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.

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