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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 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?
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?
12. When a coin is thrown we have the possible outcome of a head or a tail. And when a dice is thrown we have the possible outcomes 1, 2, 3, 4, 5 and 6. So, the desired sample space is
S = {T, (H, 1), (H, 2, 1), (H, 2, 2), (H, 2, 3), (H, 2, 4), (H, 2, 5), (H, 2, 6), (H, 3), (H,
Upvote 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.
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.
11. Let us denote the non-defective and defective bulbs by 'N' and 'D'. So, that the sample space of selecting 3 bulbs from a lot is.
S = {NNN, NND, NDN, DNN, DDN, NDD, DND, DDD}
Upvote 11. An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
11. An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
11. The possible outcomes when a coin is tossed is a Head or a Tail. And the possible outcomes when a die is rolled is 1, 2, 3, 4, 5 or 6.
By condition, when a head occurs or first toss the coin is tossed again and if a tail occurs on first toss a die is rolled. So, the required sample space is
S
Upvote