Question

A student takes a true-false test that has 8 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(6 or more)

0.0352

0.6367

0.3633

0.1445

Answer 1

CORRECT ANSWER= 0.1445

Since it is a true false test

P = 0.5

binomial probability

nCx = n! / [(n-x)!*x!]

Binomial Probability = nCx * (p)x * (q)n-x,

where,

n = number of trials

x = number of successes.

n = 8, p = 0.5, q = 1 – p = 0.5

P(X 6) = P(6) + P(7) + P(8)

P(X = 6) = 8C6 * (0.5)6 * (0.5)8-6 = 0.1094

P(X = 7) = 8C7 * (0.5)7 * (0.5)8-7 = 0.0313

P(X = 8) = 8C8 * (0.5)8 * (0.5)8-8 = 0.0039

P(X 6) = .0.1094 + 0.0313 + 0.0039 = 0.1445

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