# Question about Binominal Probability

Hello everyone. Could you guys help me with a Quants question about binominal probabilities?

In fact its quite an easy question, but im kind of getting confused here when faced whit the question below.

For a certain class of junk bonds, the probability of default in a given year is 0.2. Whether one bond defaults is independent of whether another bond defaults. For a portfolio of five of these junk bonds, what is the probability that zero or one bond of the five defaults in the year ahead?

A) 0.0819. B) 0.7373. C) 0.4096.

The correct answer was B) 0.7373.

Although the formula is p^x(1-p)^n-x, the result presented its 0.7373 while my calculations lead me to 0.4096:

P(0)=0,8^5

P(1)=0,8^4x0,2

P(1 or 0) = 0,3277 + 0,0819 = 0,4096.

What am i doing wrong here?

Thanks!

Multiply the 0.0819 by 5. The formular is nCx P^x(1-P)^n-x. You missed only the nCx part and 5C1 is 5

You forget part of the formula; it’s

**(nCx)**p^x(1-p)^(n-x)

5C1 = 5, so you should calculate:

P(1 or 0) = 0,3277 + 5 × 0,0819 = 0,7373.