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At summer camp, 40 students are divided into two groups for swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking.

| Outcome | Frequency |
|----------|-----------|
| Swimming | 12 |
| Hiking | 28 |

Compare the probabilities and determine which statement is true.

A. The theoretical probability of swimming, P(swimming), is [tex]\(\frac{1}{2}\)[/tex], but the experimental probability is [tex]\(\frac{12}{40}\)[/tex].

B. The theoretical probability of swimming, P(swimming), is [tex]\(\frac{12}{28}\)[/tex], but the experimental probability is [tex]\(\frac{1}{2}\)[/tex].

C. The theoretical probability of swimming, P(swimming), is [tex]\(\frac{28}{40}\)[/tex], but the experimental probability is [tex]\(\frac{1}{2}\)[/tex].



Answer :

GinnyAnswer
Let's delve into the problem step-by-step to understand the theoretical and experimental probabilities of a student being assigned to swimming or hiking at the summer camp.

1. Theoretical Probability of Swimming:
- Each camper flips a coin to decide whether they will swim or hike.
- Since a fair coin has two possible outcomes (heads or tails), and assuming the result of heads means swimming and tails means hiking, the probability of either outcome (swimming or hiking) is equal.
- Therefore, the theoretical probability of swimming is [tex]\( \frac{1}{2} \)[/tex] or 0.5.

2. Experimental Probability of Swimming:
- We have been given that out of 40 students, 12 chose swimming.
- The experimental probability is calculated as the number of successful outcomes (students swimming) divided by the total number of trials (total students).
- Therefore, the experimental probability of swimming is [tex]\( \frac{12}{40} \)[/tex].

3. Comparison of Probabilities:
- The theoretical probability of swimming [tex]\( P(\text{swimming}) \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
- The experimental probability of swimming is [tex]\( \frac{12}{40} \)[/tex], which simplifies to 0.3.

4. Conclusion:
- The theoretical probability of swimming is [tex]\( \frac{1}{2} \)[/tex] or 0.5.
- The experimental probability of swimming is [tex]\( \frac{12}{40} \)[/tex] or 0.3.

Given these calculations, the correct statement is:
- "The theoretical probability of swimming, [tex]\( P(\text{swimming}) \)[/tex], is [tex]\( \frac{1}{2} \)[/tex], but the experimental probability is [tex]\( \frac{12}{40} \)[/tex]."

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