In 10th grade worksheet on probability we will practice various types of problems based on definition of probability and the theoretical probability or classical probability.

**1.** Write down the total number of possible outcomes when the
ball is drawn from a bag containing 5 red balls, 3 black balls and 4 green
balls.

**2. Fill in the blanks.**

(i) The probability of an event is less than or equal to ....... but greater than or equal to....... .

(ii) If E is an event then P(E) + P(\(\overline{E}\)) = ....... .

(iii) The probability of a sure event is ....... .

(iv) The probability of an impossible event is ....... .

**3.** A survey was conducted on 1200 families and the number of children in each family was recorded. The results are given below:

**No. Of Children**

0

1

2

3

4

5

**Total**

**No. of Families**

42

446

534

115

52

11

**1200**

If a family is chosen at random, find the probability that it will have

(i) exactly 2 children

(ii) less than 2 children

(iii) more than 3 children

(iv) no children

**4.** A survey was conducted on 1500 family having 2 children each. The results obtained are given below:

**No. of Girl children**

2

1

0

**Total**

**No. of families**

475

815

210

**1500**

If one family is selected at random, find the probability that it will have

(i) no girl child

(ii) at least one girl child

(iii) no boy child

**5.** Seeds were kept in 5 containers to germinate. Each container contained 100 seeds. After 20 days the germinated seeds were counted and the results were recorded as shown below:

**Container Number**

1

2

3

4

5

** Number of germinated Seeds**

83

72

90

76

84

If a container is selected at random from then, find the probability of finding

(i) less than 70 germinated seeds

(ii) more than 72 germinated seeds

(iii) more than 70 germinated seeds

(iv) at least 83 germinated seeds

**6.** The marks scored by 100 students are given below:

**Overlapping Intervals of Marks Scored**

0 - 20

20 - 40

40 - 60

60 - 80

80 - 100

**Total**

**Number of Students**

8

13

37

32

10

**100**

Find the probability of s student scoring

(i) less than 20

(ii) below 60 but not below 40

(iii) less than 40

(iv) more than or equal to 60

(v) below 80.

**7.** A bag contains 8 red marbles and 6 white marbles. A marble
is picked up at random. Find the probability of

(i) getting a red marble

(ii) getting a marble which is not red

**8.** A box contains 5 red marbles, 7 black marbles and 3 white
marbles. One marble is taken out from the box at random. What is the
probability that the marble taken out will be

(i) black

(ii) red

(iii) not white

(iv) black or white

**9.** Find the probability that a number selected at random
from the numbers 1, 2, 3, 4, ....., 34, 35 is a

(i) prime number

(ii) multiple of 7

(iii) divisible by 3 and 5

(iv) multiple of 3 or 5

(v) not a multiple of 7.

**10.** A bag contains 6 red balls, 8 wite balls, 5 green balls
and 3 balls. One ball is drawn at random from the bag. Find the probability
that the ball drawn is

(i) white

(ii) black or red

(iii) not white

(iv) neither white nor black

**11.** In a lottery there are 5 prizes and 45 blanks. Sophie
has one ticket for the lottery. What is the chance (probability) that Sophie

(i) will get a prize

(ii) will not get a prize?

Also verify that the sum of the probabilities in (i) and (ii) is 1.

**12.** A box contains 19 balls bearing numbers from 1 to 19. A
ball is drawn at random from the box. Find the probability that the number on
the ball is

(i) a composite number

(ii) divisible by 3 or 4

(iii) divisible neither by 5 nor by 10

(iv) an even number

**13.** There are two children in a family. Find the probability
that there is at least one girl in the family.

**14.** In a class there are 35 boys and 15 girls. What is the
probability of a randomly selected student of the class to be a girl?

**15.** Find the probability of getting 53 Mondays in a non-leap
year.

**16.** Find the probability of getting 53 Fridays in a leap
year.

**17.** Find the probability of getting 52 Saturdays in a leap
year.

**18.** If the probability of India winning the next Cricket
World Cup is 0.25, what is the probability India not winning the next Cricket
World Cup?

**19.** In an experiment there are exactly three elementary
events. The probabilities of two of them are \(\frac{2}{9}\) and \(\frac{3}{9}\)
respectively. What is the probability of the third elementary event?

Note: The sum of all the elementary events is 1.

Answers on 10th grade worksheet on probability are given below to check the exact answers of the questions.

**Answers**

**1.** 12

**2.** (i) 1, 0 respectively.

(ii) 1

(iii) 1

(iv) 0

**3.** (i) \(\frac{89}{200}\)

(ii) \(\frac{61}{150}\)

(iii) \(\frac{21}{400}\)

(iv) \(\frac{7}{200}\)

**4.** (i) \(\frac{7}{50}\)

(ii) \(\frac{43}{50}\)

(iii) \(\frac{19}{60}\)

**5.** (i) 0

(ii) \(\frac{4}{5}\)

(iii) 1

(iv) \(\frac{1}{2}\)

**6.** (i) \(\frac{2}{25}\)

(ii) \(\frac{37}{100}\)

(iii) \(\frac{21}{100}\)

(iv) \(\frac{21}{50}\)

(v) \(\frac{9}{10}\)

**7.** (i) \(\frac{4}{7}\)

(ii) \(\frac{3}{7}\)

**8.** (i) \(\frac{7}{15}\)

(ii) \(\frac{1}{3}\)

(iii) \(\frac{4}{5}\)

(iv) \(\frac{2}{3}\)

**9.** (i) \(\frac{11}{35}\)

(ii) \(\frac{1}{7}\)

(iii) \(\frac{2}{35}\)

(iv) \(\frac{16}{35}\)

(v) \(\frac{6}{7}\)

**Hint:** Multiples of 3 or 5 are 3, 6, 9, 12, 15, 18, 21, 24,
27, 30, 33, 5, 10, 20, 25, 35.

**10.** (i) \(\frac{4}{11}\)

(ii) \(\frac{9}{22}\)

(iii) \(\frac{7}{11}\)

(iv) \(\frac{1}{2}\)

**11.** (i) \(\frac{1}{10}\)

(ii) \(\frac{9}{10}\)

**12.** (i) \(\frac{10}{19}\)

(ii) \(\frac{9}{19}\)

(iii) \(\frac{16}{19}\)

(iv) \(\frac{9}{19}\)

**13.** \(\frac{3}{4}\)

**14.** \(\frac{3}{10}\)

**15.** \(\frac{1}{7}\)

**16.** \(\frac{2}{7}\)

**17.** \(\frac{5}{7}\)

**18.** \(\frac{3}{4}\)

**19.** \(\frac{4}{9}\)

**Hint:** The sum of all the elementary events is 1.

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