Question

A quiz consists of 10 multiple-choice questions. Each question has 5 possible answers, only one of which is correct. Pat plans to guess the answer to each question. Find the probability that Pat gets

a. one answer correct.

b. all 10 answers correct.

Answer 1

Using the binomial theorem of:

(p + q)^n = Σ nCr p^r q^(n-r) with r = 0, 1, ..., n

Each term gives the probability of r successes P(r) out of n trials: p is the probability of success and q = 1 - p is the probability of failure for each trial; for this question:

p = 1/5

q = 4/5

n = 10

and to get the probability of

a. one answer correct.

p(1)=10C1 p^1 q^9

using excell =BINOM.DIST(1,10,0.2,0)

0.2684

b. all 10 answers correct.

p(10)=10C10 p^10 q^0

using excell =BINOM.DIST(10,10,0.2,0)

=1.024E-07

=0