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Answer:
0.1333 = 13.33% probability that bridge B was used.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Arrives home by 6 pm
Event B: Bridge B used.
Probability of arriving home by 6 pm:
75% of 1/3(Bridge A)
60% of 1/6(Bridge B)
80% of 1/2(Bridge C)
So
Probability of arriving home by 6 pm using Bridge B:
60% of 1/6. So
Find the probability that bridge B was used.
0.1333 = 13.33% probability that bridge B was used.