Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

A financial risk manager has three routes to get to the office. The probability that she gets to the office on time using routes X, Y, and Z are 60%, 65%, and 70%. She does not have a preferred route and is therefore equally likely to choose any of the three routes. Calculate the probability that she chose route Z given that she arrives to work on time.

Exam-Like

Community

TTanishq

0.359

0.233

0.216

0.2

Explanation:

This is a conditional probability problem that can be solved using Bayes' theorem.

Let:

X, Y, Z be events of choosing routes X, Y, Z respectively
O be the event of arriving on time

Given:

P(O|X) = 0.60
P(O|Y) = 0.65
P(O|Z) = 0.70
P(X) = P(Y) = P(Z) = 1/3 (equally likely routes)

We want P(Z|O):

$P(Z|O) = \frac{P(Z) \cdot P(O|Z)}{P(Z) \cdot P(O|Z) + P(Y) \cdot P(O|Y) + P(X) \cdot P(O|X)}$

$= \frac{(\frac{1}{3} \cdot 0.7)}{(\frac{1}{3} \cdot 0.7) + (\frac{1}{3} \cdot 0.65) + (\frac{1}{3} \cdot 0.6)}$

$= \frac{0.2333}{(0.2333 + 0.2167 + 0.2)}$

$= \frac{0.2333}{0.65} = 0.3589 \approx 0.359$

The calculation shows that given she arrived on time, the probability she took route Z is approximately 0.359.

Powered ByGPT-5.2

Comments

Loading comments...