Take a guess: A student takes a multiple-choice test that has 12 questions. Each question has six 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 6:

Answer:
Given:

Probability of success $(p) = \frac{1}{6} = 0.1667 $

Sample size $(n) = 12 $

Solution:
The probability that x is equal to 6:
$P(x = 6) = \binom{12}{6} \cdot 0.1667^6 \cdot (1 – 0.1667)^{12-6} = 0.0066$

Final Answer:
The probability that x is equal to 6 = 0.0066

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