## Mock test 2

AMITAG1990
Finance Junkie
Posts: 89
Joined: Sat Sep 22, 2012 12:35 pm

### Mock test 2

An investor is holding a portfolio of 10 BBB-rated bonds. The probability that a bond will be defaulted is 0.25. The default between the bonds is independent. What is the probability that at least 4 bonds will not be defaulted?
Choose one answer.
a. 0.2241 Correct
b. 0.3478 Incorrect
c. 0.7759 Incorrect
d. 0.6522 Incorrect
The correct answer is 0.2241
.
Explanation..
Default on bonds follows a binomial distribution where the probability of default is (0.25) and the total number of bonds is 10.
Let the probability of no-default on the number bonds [[yes]] be p[[yes]].
Therefore, probability that the bonds will be defaulted = 1 – [p(0) + p(1) + p(2) + p(3)] = 1 - [(3/4)10 + 10 × (1/4) × (3/4)9 + 45 × (1/4)2 × (3/4)8 + 120 × (1/4)3 × (3/4)7] = 0.2241

But if we have to find a prob. of not defaulting at least 4 bond then we should find a prob. of default of 6 or less than 6 bond and minus it from 1.
=1-P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)... if given ans is right than please once explain me.

balajismz
Finance Junkie
Posts: 63
Joined: Mon Nov 05, 2012 9:13 am

### Re: Mock test 2

Right, the approach is correct,l but you will have to use prob of not deftaulting as p

Balaji

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