Question 30
Question: A card is drawn from a well-shuffled pack of cards and its suit is noted. (spade, clubs, hearts or diamond). This trial is repeated 400 times and the Number of times each suit is drawn is given below.
When a card is drawn at random what is the probability that it is
1) a diamond
2) a black card
3) not a spade
Answer:
1) Total number of trials = 400
Number of trials in which a diamond showed up = 76
P (the card drawn is a diamond)
2) Number of times a black card showed up = 96 + 108 = 204
P (the card drawn is black)
3) Number of times a card other than a spade showed up = 108 + 120 + 76 = 304
P (the card is not a spade)
Question 31
Question: The monthly wages of 200 workers in a factory is given by the following table:
If one worker in the factory is chosen at random, what is the probability that
1) his wage is in the range Rs. 3500 - 4500?
2) his wage is Rs. 4000 or above?
3) Give two events in the content, one having probability 0 and the other having probability 1.
Answer: Total number of workers = 200
1) Number of workers whose wage is between Rs. 3500 and Rs. 4500
= 63 + 42 = 105
P (the worker's wage is between Rs. 3500 and Rs. 4500)
2) Number of workers with wage above Rs. 4000
= 42 + 19 = 61
P (the worker's wage is above Rs. 4000)
3) Let E1 be the event "the wage of the worker is less than Rs. 3000".
Since there is no worker whose wage is less than Rs. 3000, P(E1) = 0.
Let E2 be the event: "the wage is not less than Rs. 3000".
As the wages of all the workers considered is greater than or equal to Rs. 3000, P(E2) = 1
Question 32
Question: In a cricket match, the number of dot-balls bowled in an over was noted down in the first 30 overs as follows:
What is the probability that an over bowled in the match?
1) has no dot balls
2) has not more than 2 dot balls
3) at least two dot balls?
Answer: Total number of overs = 30
1) Number of overs with no dot balls = 7
P (the over has no dot balls) 
2) Number of overs with not more than 2 dot balls = 7 + 5+ 5 = 17
P (the over has not more than 2 dot balls) 
3) Number of overs with atleast 2 dot balls = 5 + 4 + 3 + 3 + 3 = 18
P (the over has atleast 2 dot balls) 
Question 33
Question: 100 mangoes are selected at random from each of 5 baskets of mangoes, and the number of mangoes which are spoilt is counted and recorded as follows:
When one such basket is checked what is the probability that it has
1) no spoilt mangoes
2) Atleast 10 spoilt mangoes
3) more than 20 spoilt mangoes
Answer: Number of baskets = 5
1) Number of baskets with no spoilt mangoes = 0
P (the basket has no spoilt mangoes) = 0
2) No of basket has no spoilt mangoes = 5
P (the basket has at least 10 spoilt mangoes) =1
3) No of baskets with more than 20 spoilt mangoes = 3
P(the basket has more than 20 spoilt mangoes)
Question 34
Question: Consider the following frequency distribution table which gives the heights of 40 students in a class
Find the probability that the height of a student in the class
1) lies in the interval 150 - 155
2) is 145 cm or above 145 cm
3) is below 150 cm
Answer: Total Number of students = 40
1) Number of students whose height lies in the interval 150 - 155 cm = 12
P (the height of the student is in the interval 150 - 155) 
2) Number of students whose height is 145 cm or above 145 cm
= 11 +12 + 9 = 32
P (the height of the student is 145 cm or above) 
3) Number of students whose height is below 150 cm= 8 + 11 = 19
P (the height of the student is less than 150 cm) 
Question 35
Question: Cards numbered 1 to 10 are placed in a box. One card is drawn and the number noted. This trial is repeated 500 times and the result is tabulated as follows:
If a card is drawn what is the probability that the card no is
1) a prime number
2) an even number
3) not less than 8
Answer: Number of trials = 500
1) Number of trials in which the card drawn has a prime number
= 34 + 52 + 54 + 60 = 200
P(the card number is prime) 
2)Number of trials in which the card drawn has an even number
= 34 + 48 + 36 + 62 + 70 = 250
P(the card number is even) 
3)Number of trials in which the card number is greater than 6
= 60 + 62 + 56 + 70 = 248
P (card number is greater than 6) 
4) Number of trials in which the card number is not less than 8
= 62 + 56 + 70 = 188
P (card number is not less than 8) 
Question 36
Question: An organisation selected 2400 families at random and surveyed than 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 - Rs. 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 not owning any vehicle iv) earning Rs. 13000 - 16000 per month and owning more than 2 vehicles v) owning not more than 1 vehicle.
Answer: Total number of families = 2400
i) Number of families earning Rs. 10000 - Rs. 13000,
and owning 2 vehicles = 29
P (the family is earning Rs. 10000 - Rs. 13000 and owns 2 vehicles)
ii) Number of families earning Rs. 16000 or more
and owning 1 vehicle = 579
P (the family is earning Rs. 16000 or more and own 1 vehicle)
iii) Number of families earning less than Rs.7000
and not owning any vehicle = 10
P (the family is earning less than Rs. 7000 and does not own any vehicle)
iv) Number of families Rs. 13000 - Rs. 16000
and owning more than 2 vehicles =25
P (the family is earning Rs. 13000 - Rs. 16000 and owns more than 2 vehicles)
v) Number of families owning not more than 1 vehicle
= 10 + 10 + 1 + 2 + 1 + 160 +305 +535 +469 +579 = 2062
P (the family owns not more than 1 vehicle)
Question 37
Question: If E1, E2, E3 cover all possible outcomes of a trial, and P(E1) = 0.7, P (E2) = 0.05. What is the probability of E3?
Answer: P(E1) + P(E2) + P(E3) = 1 P(E3) = 1 - (0.7 + 0.05)
= 1 - 0.75 = 0.25
Question 38
Question: In a survey conducted among 300 students each of whom could speak either Hindi or English or both, it was found that 200 of them could speak Hindi and 250 of them could speak English. If a student is selected at random, what is the probability that he can speak both the languages?
Answer: Total number of students = 300
Number of students who can speak both languages
= 200 + 250 - 300 = 150 P (the student can speak both languages)
