Question Video: Determining the Probability of an Event Mathematics

A card is selected at random from a pack of 45 cards which are numbered 1 to 45. What is the probability that the selected card has a perfect square number?

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Video Transcript

A card is selected at random from a pack of 45 cards which are numbered one to 45. What is the probability that the selected card has a perfect square number?

We begin by recalling that probability is the likelihood or chance of an event occurring. We can write this probability as a fraction, where the numerator is the number of favorable outcomes and the denominator is the total number of outcomes. In this question, there are 45 cards in total. Therefore, the denominator, the total number of cards, will be 45. We are asked to find the probability of selecting a perfect square number, which means that the numerator will be the number of square numbers between one and 45. The perfect squares are the squares of the whole numbers. The first 10 are one, four, nine, 16, 25, 36, 49, 64, 81, and 100. These are the answers to one multiplied by one, two multiplied by two, three multiplied by three, and so on.

In this question, we are interested in the square numbers between one and 45. There are six of these: one, four, nine, 16, 25, and 36. The probability of selecting a perfect square number from the set of cards is therefore equal to six out of 45. We can simplify this fraction by dividing our numerator and denominator by three. Six divided by three is two, and 45 divided by three is 15. The probability of selecting a card that has a perfect square number is two out of 15 or two fifteenths.

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