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 a number less than 4.Event B: The marble selected has an odd number.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 a number less than 4.Event B: The marble selected has an odd number.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 the numbers less than 4, which are 1, 2, and 3. Event B includes all odd numbers, which are 1, 3, 5, and 7. Combining these gives the outcomes for "A or B" as 1, 2, 3, 5, 7.
(b) Event "A and B": This event includes all outcomes that are in both event A and event B. Looking at the outcomes for events A and B, the numbers that are in both sets are 1 and 3. So, the outcomes for "A and B" are 1, 3.
(c) The complement of the event A: The complement of an event includes all outcomes that are not in the event. Event A includes the numbers 1, 2, and 3. So, the complement of A includes all the other numbers, which are 4, 5, 6, 7, 8.
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