A marble is selected from a bag containing eight marbles numbered 1 to 8.The number on the marble selected will be recorded as the outcome.Consider the following events.Event A: The marble selected has an even number.Event B: The marble selected has a number from 3 to 6.Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.(a) Event"AorB":(b) Event"AandB":(c) The complement of the event A:
Question
A marble is selected from a bag containing eight marbles numbered 1 to 8.The number on the marble selected will be recorded as the outcome.Consider the following events.Event A: The marble selected has an even number.Event B: The marble selected has a number from 3 to 6.Give the outcomes for each of the following events.If there is more than one element in the set, separate them with commas.(a) Event"AorB":(b) Event"AandB":(c) The complement of the event A:
Solution
(a) Event "A or B": This event includes all outcomes that are in either Event A or Event B. Event A includes all even numbers (2, 4, 6, 8) and Event B includes numbers from 3 to 6 (3, 4, 5, 6). So, the outcomes for "A or B" are 2, 3, 4, 5, 6, 8.
(b) Event "A and B": This event includes all outcomes that are in both Event A and Event B. The only numbers that are both even (Event A) and between 3 and 6 (Event B) are 4 and 6. So, the outcomes for "A and B" are 4, 6.
(c) The complement of the event A: The complement of an event includes all outcomes that are not in the event. Event A includes all even numbers (2, 4, 6, 8), so the complement of Event A includes all odd numbers. So, the outcomes for the complement of A are 1, 3, 5, 7.
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