Refer to Exercise 23. Assume that the probabilities that each of the three scenarios occurs are P(A) = 0.20, P(B) = 0.30, and P(C) = 0.50.

a. Find the probability that scenario A occurs and that the loss is 5%.

b. Find the probability that the loss is 5%.

c. Find the probability that scenario A occurs given that the loss is 5%.

Answer:

Step 1 of 4:

Assume that the probabilities that each of the three scenarios occurs are P(A) = 0.20, P(B) = 0.30, P(C) = 0.50.

Step 2 of 4:

a). In exercise 23, the table is

Probability |
|||

Loss (%) |
Scenarios A |
Scenarios B |
Scenarios C |

0 |
0.65 |
0.65 |
0.65 |

2 |
0 |
0 |
0.24 |

5 |
0.2 |
0.24 |
0.1 |

10 |
0 |
0 |
0.01 |

15 |
0.1 |
0.1 |
0 |

20 |
0 |
0.01 |
0 |

25 |
0.05 |
0 |
0 |

To find the probability that scenario A occurs and that the loss is 5%.

Here, using the formula for conditional probability.

Now,

Let ‘L’ denote the loss.

=

= (0.20)(0.2)

= 0.04

(In the table, 5% loss for scenario A is 0.2. So = 0.2 )

Therefore, the probability that scenario A occurs and that the loss is 5% is 0.04.