Question Video: Writing the Subset of the Sample Space Representing the Intersection of Two Events

A card is drawn at random from a pack of cards numbered from 1 to 32. Write the set of outcomes that the number on the card is odd and divisible by 3?

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Video Transcript

A card is drawn at random from a pack of cards numbered from one to 32. Write the set of outcomes that the number on the card is odd and divisible by three.

Let’s first consider all the numbers from one to 32. The first part of the question stipulated that the number had to be odd. This immediately rules out all the even numbers. Our only possible outcomes so far are the odd numbers.

Our second stipulation was that the number had to be divisible by three. This means the number has to be in the three times table. The numbers circled are all in the three times table. However, we’ve already ruled out six, 12, 18, 24, and 30, as they are even numbers.

Which of the numbers in the list are odd and also divisible by three? Well, in the first row, the only number is three. In the second row, we have nine and 15. In the third row, we have 21. And in the final row, we have 27. This means that the set of outcomes that are odd and divisible by three from cards numbered one to 32 are three, nine, 15, 21, and 27. There are only five possible outcomes.

We could therefore say that the probability of selecting a number that is odd and divisible by three is five out of 32.

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