Question

a set of cards contains the numbers 1 through 20. mathieu chooses a card at random, records the number of the card, and then returns the card to the set. he conducts 200 trials of this event. based on the theoretical probability, how many times can mathieu expect to choose a multiple of 5?

Explanation:

Step1: Determine the theoretical probability

The numbers from 1 - 20. The multiples of 5 are 5, 10, 15, 20. So there are 4 favorable outcomes. The total number of outcomes is 20. The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P = \frac{4}{20}=\frac{1}{5}\)

Step2: Calculate the expected number of times

We use the formula \(E = n\times P\), where \(n = 200\) (number of trials) and \(P=\frac{1}{5}\). So \(E=200\times\frac{1}{5}\)

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Answer:

40