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22. 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) A′ (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) A ∩ B′ ∩ C′
22. 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) A′ (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) A ∩ B′ ∩ C′
22. The sample space of the experiment is
S = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4
Upvote 
21. Three coins are tossed. Describe
(i) Two events which are mutually exclusive.
(ii) Three events which are mutually exclusive and exhaustive.
(iii) Two events, which are not mutually exclusive.
(iv) Two events which are mutually exclusive but not exhaustive.
(v) Three events which are mutually exclusive but not exhaustive.
21. Three coins are tossed. Describe
(i) Two events which are mutually exclusive.
(ii) Three events which are mutually exclusive and exhaustive.
(iii) Two events, which are not mutually exclusive.
(iv) Two events which are mutually exclusive but not exhaustive.
(v) Three events which are mutually exclusive but not exhaustive.
21. The sample space of the experiment is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
(i) Let A and B be two events such that
A: only head occurs
A = {HHH}
B: only tail occurs
B = {TTT}
And A ∩B = {HHH}∩ {TTT} =∅
(ii) Let A, B and C be two events such that
A: at most one head (i.e., the event in which we
Upvote 20. 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?
20. 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?
20. The sample space of the experiment is
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Now, A = {HHH}
B = {HHT, HTH, THH}
C = {TTT}
D = {HHH, HHT, HTH, HTT}
(i) A∩ B = {HHH}∩ {HHT, HTH, THH} =∅
A ∩ C = {HHH}∩ {TTT} =∅
A∩ D = {HHH}∩ {HHH, HTH, HTT} = {HHH}
B ∩ C = {HHT, HTH, THH}∩ {TTT} =∅
B∩ D = {HHT, HTH, T
Upvote 19. 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?
19. 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?
19. The sample space of the experiment is
S = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (
Upvote 18. 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 A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F′, F′
18. 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 A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F′, F′
18. The sample space of the experiment is
S = {1, 2, 3, 4, 5, 6}
(i) A = {1, 2, 3, 4, 5, 6}
(ii) B =∅
(iii) C = {3, 6}
(iv) D = {1, 2, 3}
(v) E = {6}
(vi) F = {3, 4, 5, 6}
A ∪ B = {1, 2, 3, 4, 5, 6}∩ {∅}= ∅h
= {1, 2, 3, 4, 5, 6}
A ∩B = {1, 2, 3, 4, 5, 6}∩ {∅}
B ∪C = ∅∪ {3,
Upvote 17. 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?
17. 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?
17. The sample space of the experiment is
S = {1, 2, 3, 4, 5, 6} and E = {4}
F = {2, 4, 6}
So, E∩ F = {4} ∩ {2, 4, 6} = {4} ≠
Therefore E and F are not mutually exclusive.
Upvote 16. A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
16. A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
16. When a die is drawn we can have 1, 2, 3, 4, 5 and 6. So, sample space of throwing dice until a six comes up is
S = { (6, (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (1, 6), (1, 2, 6), (1, 3, 6), (1, 4, 6), (1, 5, 6), (1, 6)……., (1, 5, 6), (1, 6)……… (1, 5, 6)………}
Hence, the samp
Upvote 15. A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.
15. A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.
15. The possible outcome when a coin is tossed is a head or a tail. When a dice is thrown we can have the possible outcomes 1, 2, 3, 4, 5 and 6. Let R1, R2 be the two red balls and B1, B2, B3 be the two black balls. So, the desired sample space is
S = { (T, R1), (T, R2), (T, B1), (T, B2), (T
Upvote 14. An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
14. An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
14. The possible outcome when a coin is tossed is a head or a tail. When a die is thrown we can have the possible outcome 1, 2, 3, 4, 5 and 6. So, the desired sample space is
S = { (2, H), (2, T), (4, H), (4, T), (6, H), (6, T), (1, H, H), (1, H, T), (1, T, H), (1, T, T), (3, H, H), (3, H, T), (3
Upvote 13. The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.
13. The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.
13. The possible numbers to be chosen are 1, 2, 3 and 4. The sample space of drawing two slips one after another without replacement is
S = { (1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}
Upvote