Financial Risk Manager Part 1
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A mathematician has given you the following conditional probabilities:
- p(O|T) = Conditional probability of reaching the office if the train arrives on time 0.62
- p(O|T c) = Conditional probability of reaching the office if the train does not arrive on time 0.47
- p(T) = Unconditional probability of the train arriving on time 0.65
- p(O) = ? Unconditional probability of reaching the office
What is the unconditional probability of reaching the office, p(O)?
Other
Community
NNikitesh
A
0.5675
B
0.4325
C
0.3265
D
0.3333
Explanation:
This question can be solved using the total probability rule.
If p(T) = 0.65 (Unconditional probability of train arriving on time is 0.65), then the unconditional probability of the train not arriving on time p(T c) = 1 - p(T) = 1 - 0.65 = 0.35.
Now, we can solve for p(O) = p(O|T) * p(T) + p(O|T c) * p(T c) = 0.62 * 0.65 + 0.47 * 0.35 = 0.5675
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