Chai walks to college 60% of the time. Vy does the same 30% of the time. Considering these events as independent, the probability that both students walk to college is:

Question

BlackTom AI · Accepted Answer

For independent events, P(both occur) = P(A) × P(B). Here Chai walking and Vy walking are treated as independent events.

1) Relevant knowledge points and concepts
- Independence: if two events are independent, the probability they both happen equals the product of their individual probabilities.
- Converting percentages to decimals or fractions makes multiplication straightforward.
- Avoid adding probabilities when the question asks for a joint (both) event.

2) Step-by-step reasoning
- Convert the given percentages to decimals: 60% = 0.60, 30% = 0.30.
- Apply the independence rule: P(Chai and Vy walk) = P(Chai walks) × P(Vy walks).

3) Calculations with intermediate steps
- In decimals: 0.60 × 0.30 = 0.18.
- As fractions: 60% = 3/5, 30% = 3/10. Multiply: (3/5) × (3/10) = 9/50 = 0.18.
- In percent terms: 60% of 30% = 18%.

4) Why the correct answer is correct
- Multiplication gives the probability that both independent events occur on the same trial (or day). The product 0.18 means there is an 18% chance both students walk on the same occasion.

5) Why the other options are incorrect
- A (0.60): equals only Chai’s probability, not the joint probability.
- B (0.90): this would be the sum 0.60 + 0.30, which is not the rule for joint probability and would exceed 1 if events were larger; addition applies to "either/or" under certain conditions, not "both" for independent events.
- D (0.30): equals only Vy’s probability, not the joint probability.

6) Conclusion
The probability both students walk to college, assuming independence, is 0.18. This matches the provided correct answer C. 0.18.

Chai walks to college 60% of the time. Vy does the same 30% of the time. Considering these events as independent, the probability that both students walk to college is:单项选择题

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