Take a guess: A student takes a multiple-choice test that has 15 questions. Each question has three 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 7:

Answer:
Given:

Probability of success $(p) = \frac{1}{3} = 0.3333 $

Sample size $(n) = 15 $

Solution:
The probability that x is equal to 7:
$P(x = 7) = \binom{15}{7} \cdot 0.3333^7 \cdot (1 – 0.3333)^{15-7} = 0.1148$

Final Answer:
The probability that x is equal to 7 = 0.1148

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