Question

A student is making independent random guesses on a test. The probability the student guess correctly is 0.25 for each question. Assume that the guesses are independent. Find the probability of 2 or more are correct in 10 guesses.

Answer 1

Solution

Given that ,

p = 0.25

q = 1 - p = 1 - 0.25 = 0.75

n = 10

Using binomial probability formula ,

P(X = x) = (n C x) * p x * (1 - p)n - x

P(X $\geq$ 2 ) = 1 - P( x <2)

= 1 - P(X = 0) - P(X = 1)

= 1 - (10 C 0) * 0.25 0 * (0.75)10 - (10 C 1) * 0.25 1 * (0.75)9

=1-0.2440

probability=0.7560