a set of cards contains the numbers 1 through 20. mathieu chooses a card at random, records the number of…
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?\n10\n20\n40\n50
Answer
Explanation:
Step1: Find number of multiples of 5
The multiples of 5 from 1 - 20 are 5, 10, 15, 20. So there are 4 such numbers.
Step2: Calculate theoretical probability
The total number of cards is 20. The theoretical probability $P$ of choosing a multiple of 5 is $P=\frac{4}{20}=\frac{1}{5}$.
Step3: Calculate expected number of times
He conducts 200 trials. The expected number of times $E$ is $E = P\times n$, where $n = 200$. So $E=\frac{1}{5}\times200 = 40$.
Answer:
40