Fnd s (6).pdf • E3 = Both dice are odd, • EA = The red dice is strictly larger than the blue dice, • E, = The sum of the dice is strictly greater than 5. (a) Write out the sets corresponding to each event. (b) Determine which of the events (if any) are mutually exclusive. 4-13. The following problem is somewhat long, but interesting. Consider two standard dice, with faces {1,2, 3, 4, 5, 6}. (a) When the two dice are rolled, the sum of their values can be anything between 2 and 12. Determine the number of ways of getting a sum of 2, a sum of 3, a sum of 4, etc. (b) Consider two non-standard dice. The first has the faces {1, 2, 2, 3, 3, 4} and the second has the faces {1,3, 4, 5, 6, 8}. Once again the dice are summed, with the lowest possible value a 1, and the highest a 12. Determine the number of ways of getting a sum of 2, a sum of 3, a sum of 4, etc. (c) Comparing your numbers from (a) and (b), conclude that playing with the non-standard dice give you exactly the same outcome as playing with the two standard dice. This is the only pair of non-standard dice which give the same outcome as a standard pair. 4-14. Three fair coins are flipped and their values notes. Determine the probability of each event. 国目 195.34% 目 -0 122 (129/284)
Fnd s (6).pdf • E3 = Both dice are odd, • EA = The red dice is strictly larger than the blue dice, • E, = The sum of the dice is strictly greater than 5. (a) Write out the sets corresponding to each event. (b) Determine which of the events (if any) are mutually exclusive. 4-13. The following problem is somewhat long, but interesting. Consider two standard dice, with faces {1,2, 3, 4, 5, 6}. (a) When the two dice are rolled, the sum of their values can be anything between 2 and 12. Determine the number of ways of getting a sum of 2, a sum of 3, a sum of 4, etc. (b) Consider two non-standard dice. The first has the faces {1, 2, 2, 3, 3, 4} and the second has the faces {1,3, 4, 5, 6, 8}. Once again the dice are summed, with the lowest possible value a 1, and the highest a 12. Determine the number of ways of getting a sum of 2, a sum of 3, a sum of 4, etc. (c) Comparing your numbers from (a) and (b), conclude that playing with the non-standard dice give you exactly the same outcome as playing with the two standard dice. This is the only pair of non-standard dice which give the same outcome as a standard pair. 4-14. Three fair coins are flipped and their values notes. Determine the probability of each event. 国目 195.34% 目 -0 122 (129/284)
Question 4-13 part (c) with steps and explanations
Transcribed Image Text:Fnd
s (6).pdf
• E3 = Both dice are odd,
• EA = The red dice is strictly larger than the blue dice,
• E, = The sum of the dice is strictly greater than 5.
(a) Write out the sets corresponding to each event.
(b) Determine which of the events (if any) are mutually exclusive.
4-13. The following problem is somewhat long, but interesting. Consider two standard dice, with
faces {1,2, 3, 4, 5, 6}.
(a) When the two dice are rolled, the sum of their values can be anything between 2 and
12. Determine the number of ways of getting a sum of 2, a sum of 3, a sum of 4, etc.
(b) Consider two non-standard dice. The first has the faces {1, 2, 2, 3, 3, 4} and the second
has the faces {1,3, 4, 5, 6, 8}. Once again the dice are summed, with the lowest possible
value a 1, and the highest a 12. Determine the number of ways of getting a sum of 2, a
sum of 3, a sum of 4, etc.
(c) Comparing your numbers from (a) and (b), conclude that playing with the non-standard
dice give you exactly the same outcome as playing with the two standard dice.
This is the only pair of non-standard dice which give the same outcome as a standard pair.
4-14. Three fair coins are flipped and their values notes. Determine the probability of each event.
国目 195.34%
目 -0
122 (129/284)
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