Question 1186720: Considering the 36 possible ordered pairs of numbers (faces) when a pair of fair, six-sided dice is rolled (as the data set in Example 4.2.7 or in Example 4.2 8 of the eBook that we study), answer the following two questions:
1. Are the Event A, containing outcomes (paired data) with both values being even, and Event B, containing outcomes (paired data) with both values being odd, mutually exclusive events (disjoint events)? Show the outcomes comprising each of the two events first, then briefly support your answer to the question.
2. Are the Events C = {(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3)} and D = {(5, 1), (5, 2), (5, 3), (5, 4),
(5, 5), (5, 6)} statistically independent? Use the “Multiplication Rule” for testing statistical independence that states: if the probability of the occurrence of the shared outcome(s) between two events is equal to the product (multiplication) of the probabilities of occurrence of the two events, those two events are statistically independent.
Answer by ikleyn(52905)   (Show Source):
You can put this solution on YOUR website! .
Considering the 36 possible ordered pairs of numbers (faces) when a pair of fair, six-sided dice is rolled
(as the data set in Example 4.2.7 or in Example 4.2 8 of the eBook that we study), answer the following two questions:
1. Are the Event A, containing outcomes (paired data) with both values being even, and Event B,
containing outcomes (paired data) with both values being odd, mutually exclusive events (disjoint events)?
Show the outcomes comprising each of the two events first, then briefly support your answer to the question.
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Event A is obtaining both EVEN numbers, when a pair of six-sided dice is rolled.
Event B is obtaining both ODD numbers, when a pair of six-sided dice is rolled.
The intersection of this events is the EMPTY set, BECAUSE an even number can not be an odd number, at the same time.
So the probability of the intersection event is 0 (zero, ZERO).
Therefore, the events A and B are disjoint, or, in other words, mutually exclusive.
This conclusion is TRUE even if the pair of dice is UNFAIR.
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May I ask you PLEASE do not include several (more than one) questions into your post in the future ?
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