Video: Determining the Probability of Compound Events

A deck of cards contains cards numbered from 1 to 81. If a card is picked at random, what is the probability of picking a card that is divisible by 5?

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Video Transcript

A deck of cards contains cards numbered from one to 81. If a card is picked at random, what is the probability of picking a card that is divisible by five?

So let’s consider this deck of cards. The cards are numbered from one to 81. Because we’re considering the probability of picking a card or a particular type of card, we can use this equation. The probability of an event is equal to the number of possible outcomes over the total number of outcomes. So in this question, the probability of picking a card which is divisible by five is equal to the number of card values which are divisible by five over the total number of cards.

Let’s remember what it would mean for a value to be divisible by five. Any value that’s divisible by five means that we can divide that value by five and get an integer solution. An alternative way of thinking about it would be the values which are in the five times tables. We can list all the values here which are divisible by five. The first one would be five. The second one would be 10. And we can continue until we get to the final one of 80. We can’t go any higher because the cards only go up to 81. When we count up these values, there are 16. That means that the number of card values that are divisible by five is 16, and the total number of cards must be 81. We can’t simplify this fraction any further. So the probability of picking a card that is divisible by five is 16 over 81.

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