Question

Refer to the following scenario to solve the next four problems: A spinner that is divided into six (6) congruent regions, numbered “one” through “six”, is spun once. Let “A” be the event “odd” and “B” be the event “5”. Find each of the given probabilities.

Answer 1

To solve this problem, we first need to determine the probability of events A and B. Event A is the event "odd", so the probability of event A is 3/6, or 1/2. Event B is the event "5", so the probability of event B is 1/6.

Next, we can use the rules of probability to determine the probability of the given events. The probability of A and B occurring is the probability of event A multiplied by the probability of event B, so the probability of A and B occurring is 1/2 x 1/6 = 1/12.

The probability of either A or B occurring is the probability of event A plus the probability of event B minus the probability of A and B occurring, so the probability of either A or B occurring is 1/2 + 1/6 - 1/12 = 5/12.

The probability of A or B not occurring is the probability of the complement of A or B, which is the probability of neither A nor B occurring. The probability of neither A nor B occurring is 1 - (1/2 + 1/6 - 1/12) = 1/12.

The probability of A given B is the probability of A and B occurring divided by the probability of B occurring, so the probability of A given B is 1/12 / 1/6 = 1/2.

Therefore, the probabilities of the given events are 1/2, 5/12, 1/12, and 1/2 respectively.

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