Take a guess: A student takes a multiple-choice test that has 9 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal places. Find the probability that X is equal to 4:

Answer:
Given:

Probability of success $(p) = \frac{1}{4} = 0.25 $

Sample size $(n) = 9 $

Solution:
The probability that x is equal to 4:
$P(x = 4) = \binom{9}{4} \cdot 0.25^4 \cdot (1 – 0.25)^{9-4} = 0.1168$

Final Answer:
The probability that x is equal to 4 = 0.1168

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