Question

a set of cards contains cards numbered 1 - 8. mrs. jacobs class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. the class will conduct 1,000 trials. based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile?

Explanation:

Step1: Calculate the probability of drawing a 4

There are 8 cards in total (numbered 1 - 8). The probability of drawing a 4 is \( P(4)=\frac{1}{8} \).

Step2: Use the formula for expected value

The expected number of times a 4 is drawn in \( n = 1000 \) trials is \( E=n\times P(4) \). Substitute \( n = 1000 \) and \( P(4)=\frac{1}{8} \) into the formula: \( E = 1000\times\frac{1}{8}=\frac{1000}{8}=125 \).

Answer:

125