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.
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 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
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