Sohail brings a packed lunch to college 60% of the time. Thuy does the same 15% of the time. Considering these events as independent, the probability that both students bring a packed lunch on a particular day is:单项选择题
A
A. 0.45
B
B. 0.75
C
C. 0.60
D
D. 0.09

Question

Sohail brings a packed lunch to college 60% of the time. Thuy does the same 15% of the time. Considering these events as independent, the probability that both students bring a packed lunch on a particular day is:单项选择题

A

A. 0.45

B

B. 0.75

C

C. 0.60

D

D. 0.09

BlackTom AI · Accepted Answer

1. Relevant knowledge points and concepts
Independence of events means the probability that both occur equals the product of their individual probabilities. Percentages convert to decimals or fractions before multiplying.

2. Step-by-step reasoning
Sohail bringing a packed lunch has probability 60% and Thuy has probability 15%. Treat these as independent events, so the joint probability = P(Sohail) × P(Thuy).

3. Calculations with intermediate steps
Convert percentages to decimals:
P(Sohail) = 60% = 0.60
P(Thuy) = 15% = 0.15

Multiply the decimals:
0.60 × 0.15 = (60/100) × (15/100)
= (60 × 15) / (100 × 100)
= 900 / 10000
= 9 / 100
= 0.09

As a percentage, 0.09 = 9%.

4. Why the correct answer is correct
Because the events are independent, the joint probability calculation requires multiplication. The arithmetic above shows the product is 0.09 (9%), so the probability both bring a packed lunch on a given day is 0.09.

5. Why the other options are incorrect
A. 0.45 (45%) is too large; it would correspond to multiplying 0.60 by 0.75 or misinterpreting percentages. B. 0.75 (75%) is not a product of 0.60 and 0.15 and likely confuses addition or other unrelated values. C. 0.60 (60%) is just Sohail’s individual probability, not the joint probability. None of these match the required product 0.60 × 0.15.

6. Conclusion confirming the final answer
The correct joint probability is 0.09, which corresponds to choice D. 0.09.

Sohail brings a packed lunch to college 60% of the time. Thuy does the same 15% of the time. Considering these events as independent, the probability that both students bring a packed lunch on a particular day is:单项选择题

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