Question

question 14 (multiple choice worth 2 points) (experimental probability mc) at summer camp, 50 students are divided in two groups for swimming or hiking. each camper flips a coin, where heads represents swimming and tails represents hiking. compare the probabilities and determine which statement is true. outcome swimming hiking frequency 17 33 the theoretical probability of swimming, p(swimming), is 1/2, but the experimental probability is 17/50. the theoretical probability of swimming, p(swimming), is 1/2, but the experimental probability is 33/17. the theoretical probability of swimming, p(swimming), is 17/50, but the experimental probability is 1/2. the theoretical probability of swimming, p(swimming), is 33/17, but the experimental probability is 1/2.

Explanation:

Step1: Calculate theoretical probability

A fair - coin flip has 2 possible outcomes. The theoretical probability of getting heads (swimming) is $P(\text{swimming})=\frac{1}{2}$ since there are 2 equally - likely outcomes (heads or tails).

Step2: Calculate experimental probability

There are a total of $33 + 17=50$ trials. The number of times swimming (heads) occurred is 17. So the experimental probability of swimming is $P(\text{swimming})=\frac{17}{50}$.

Answer:

The theoretical probability of swimming, $P(\text{swimming})$, is $\frac{1}{2}$, but the experimental probability is $\frac{17}{50}$.