Question

A multiple-choice test has four questions, each with five choices for the answer. Only one of the choices is correct. You randomly guess the answer to each question. What is the probability that you answered at least one questions correctly?

A. 0.5904

B.0.1808

C.0.216

D. 0.8192

Answer 1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 1/5 = 0.2 (as only 1 is correct among five choices)

N = number of trials = 4

R = desired success = at least 1

We know that sum of all the probabilities is = 1

So, P(at least 1) = 1 - P(0)

P(at least 1) = 1 - 4c0*(0.2^0)*(1-0.2)^4-0

P(at least 1) = 0.5904