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?
10
20
40
50

Explanation:

Step1: Find number of multiples of 5

The multiples of 5 from 1 - 20 are 5, 10, 15, 20. So there are 4 multiples of 5 in the set of 20 numbers.

Step2: Calculate theoretical probability

The theoretical probability $P$ of choosing a multiple of 5 is the number of favorable outcomes (multiples of 5) divided by the total number of outcomes. So $P=\frac{4}{20}=\frac{1}{5}$.

Step3: Calculate expected number of times

The expected number of times $E$ of choosing a multiple of 5 in 200 trials is the probability of choosing a multiple of 5 times the number of trials. So $E = P\times n=\frac{1}{5}\times200 = 40$.

Answer:

C. 40