Question

A professor gives a short quiz of 10 questions; each question has four possible answers. What is the probability of getting two incorrect answers? (Use Binomial Table)

Answer 1

Solution: Given that n = 10, p = 1/4 = 0.25, X = 2

The probability of getting two incorrect answers is 0.2816

=> P(X = r) = nCr*p^r*q^(n-r)
P(X = 2) = 10C2*0.25^2*0.75^8
= 0.2816

1 Binomial distribution (n=10, p=0.25) f(x) F(x) 1 - F(x) x Pr[X = x] Pr[XSX] Pr[X> x] 0 0.0563 0.0563 0.9437 0.1877 0.2440 0.7560 2. 0.2816 0.5256 0.4744 3 0.2503 0.7759 0.2241 4 0.1460 0.9219 0.0781 5 0.0584 0.9803 0.0197 6 0.0162 0.9965 0.0035 7 0.0031 0.9996 0.0004 8 0.0004 1.0000 0.0000 9 0.0000 1.0000 0.0000 10 0.0000 1.0000 0.0000