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Conditional Probability & Bayes' Theorem · Question 93 of 125

Question 93

MediumOriginal question

In a town, 25% of the days are rainy. A bus runs late on 60% of rainy days, and it is on time on 80% of the other days. What is the probability that the bus runs late on a day picked at random?

Options for question 93

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. On the other days the bus is late with probability 1−0.8=0.21 - 0.8 = 0.2.

  2. 0.25×0.6+0.75×0.2=0.15+0.15=0.30.25 \times 0.6 + 0.75 \times 0.2 = 0.15 + 0.15 = 0.3.

Worth noting

0.75 uses 80% as the chance of running late on the other days, but 80% is the chance of being on time.

Concept
The theorem of total probability
Typical time
90 s
Your time
—
The rule this testsThe theorem of total probability
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