Page No 386:
Question 1:
Describe the sample space for the indicated experiment: A coin is tossed three times.
Page No 386:
Question 1:
Describe the sample space for the indicated experiment: A coin is tossed three times.
Page No 386:
Question 2:
Describe the sample space for the indicated experiment: A die is thrown two times.
Page No 386:
Question 3:
Describe the sample space for the indicated experiment: A coin is tossed four times.
Page No 386:
Question 4:
Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.
Page No 386:
Question 5:
Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.
Page No 386:
Question 8:
An experiment consists of recording boy-girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?
Page No 387:
Question 11:
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?
Page No 387:
Question 12:
A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?
Page No 387:
Question 16:
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
Page No 393:
Question 1:
A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?
Page No 393:
Question 2:
A die is thrown. Describe the following events:
(i) A: a number less than 7
(ii) B: a number greater than 7
(iii) C: a multiple of 3
(iv) D: a number less than 4
(v) E: an even number greater than 4
(vi) F: a number not less than 3
Also find 
Page No 393:
Question 3:
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
A: the sum is greater than 8, B: 2 occurs on either die
C: The sum is at least 7 and a multiple of 3.
Which pairs of these events are mutually exclusive?
Page No 393:
Question 4:
Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”. C denote the event “three tails show” and D denote the event ‘a head shows on the first coin”. Which events are
(i) mutually exclusive? (ii) simple? (iii) compound?
Page No 393:
Question 6:
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5
Describe the events
(i) 
(ii) not B (iii) A or B
(iv) A and B (v) A but not C (vi) B or C
(vii) B and C (viii) 
Page No 393:
Question 7:
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5
State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii) A and B are mutually exclusive and exhaustive
(iii) 
(iv) A and C are mutually exclusive
(v) A and 
are mutually exclusive
(vi) 
are mutually exclusive and exhaustive.
Page No 404:
Question 2:
A coin is tossed twice, what is the probability that at least one tail occurs?
Page No 404:
Question 3:
A die is thrown, find the probability of following events:
(i) A prime number will appear,
(ii) A number greater than or equal to 3 will appear,
(iii) A number less than or equal to one will appear,
(iv) A number more than 6 will appear,
(v) A number less than 6 will appear.
Page No 404:
Question 4:
A card is selected from a pack of 52 cards.
(a) How many points are there in the sample space?
(b) Calculate the probability that the card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) black card.
Page No 404:
Question 6:
There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
Page No 405:
Question 11:
In a lottery, person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [Hint: order of the numbers is not important.]
Page No 405:
Question 13:
Fill in the blanks in following table:
P(A) | P(B) | P(A ∩ B) | P(A ∪ B) | |
(i) |
|
|
| … |
(ii) | 0.35 | … | 0.25 | 0.6 |
(iii) | 0.5 | 0.35 | … | 0.7 |
Page No 405:
Question 15:
If E and F are events such that P(E) =
, P(F) =
and P(E and F) =
, find:(i) P(E or F), (ii) P(not E and not F).
Page No 405:
Question 19:
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?
Page No 405:
Question 20:
The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?
Page No 408:
Question 1:
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that
(i) all will be blue? (ii) atleast one will be green?
Page No 408:
Question 2:
4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
Page No 409:
Question 4:
In a certain lottery, 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) one ticket (b) two tickets (c) 10 tickets?
Page No 409:
Question 5:
Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that
(a) you both enter the same sections?
(b) you both enter the different sections?
Page No 409:
Question 8:
From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:
S. No. | Name | Sex | Age in years |
1. | Harish | M | 30 |
2. | Rohan | M | 33 |
3. | Sheetal | F | 46 |
4. | Alis | F | 28 |
5. | Salim | M | 41 |
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
Page No 409:
Question 9:
If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated? (ii) the repetition of digits is not allowed?
Page No 409:
Question 10:
The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
