Financial Risk Manager Part 1
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A mathematician has given you the following conditional probabilities:
| p(O|T) = 0.62 | Conditional probability of reaching the office if the train arrives on time | |---------------|---------------------------------------------------------------------------| | p(O|Tc) = 0.47 | Conditional probability of reaching the office if the train does not arrive on time | | p(T) = 0.65 | Unconditional probability of the train arriving on time | | p(O) = ? | Unconditional probability of reaching the office |
What is the unconditional probability of reaching the office, p(O)?
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TTanishq
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 at time is 0.65), then the unconditional probability of the train not arriving on time p(Tc) = 1 − p(T) = 1 − 0.65 = 0.35.
Now, we can solve for p(O) = p(O|T) * p(T) + p(O|Tc) * p(Tc) = 0.62 * 0.65 + 0.47 * 0.35 = 0.5675
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