Question

josh used a standard deck of 52 cards to conduct an experiment. half of the cards in the deck were red. the other half were black. josh predicted that he would choose a red card in 4 out of 8 trials. when he conducted the experiment, he actually chose a red card 6 out of 8 times. which explains the most likely reason for the discrepancy between joshs predicted and actual results?
he used too many trials for the sample space.
he incorrectly predicted the number of times he would choose a red card.
he incorrectly determined the actual number of times he chose a red card.
he used too few trials for the sample space.

Explanation:

Step1: Calculate theoretical probability

A standard deck has 52 cards, 26 red and 26 black. The theoretical probability of choosing a red card is $\frac{26}{52}=\frac{1}{2}$. In 8 trials, the predicted (theoretical) number of red - card choices is $n = 8\times\frac{1}{2}=4$.

Step2: Analyze the number of trials

The formula for experimental probability is $P=\frac{\text{number of favorable outcomes}}{\text{total number of trials}}$. When the number of trials is small, the experimental probability can deviate more from the theoretical probability. Here, the number of trials ($n = 8$) is relatively small. As the number of trials increases, the experimental probability tends to get closer to the theoretical probability.

Answer:

He used too few trials for the sample space.