A card is drawn from a set of well-shuffled identical cards numbered from 1 to 20 with no repetition. If is the the event of getting a card having an even number, is the event of getting a card having a number that is divisible by 6, and is the event of getting a card having a prime number that is greater than 17, determine the probability of or occurring.

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Example

A card is drawn from a set of well-shuffled identical cards numbered from 1 to 20 with no repetition. If is the the event of getting a card having an even number, is the event of getting a card having a number that is divisible by 6, and is the event of getting a card having a prime number that is greater than 17, determine the probability of or occurring.

Solution

The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . The cards with an even number are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, so these are the favorable outcomes for event . Find the probability of event as follows:

The probability of event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space, . The cards that are divisible by 6 are 6, 12, and 18, so these are the favorable outcomes for event . Now find the probability of event .

The notation refers to the probability of either event or event occurring, or both. If and are two non-mutually exclusive events, then , where the notation refers to the probability of events and occurring together. In this case, since all cards divisible by 6 are also cards with even numbers, must equal . Next, use this fact to help determine .

Thus, the probability of either event or event occurring is .