Introduction to probability

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Question

$A multiple choice examination has 5 questions, each question has three alternative$
$answers of which exactly one is correct. If p is the probability that a student will get 4 or$
$more correct answers just by guessing, then 3^{4} p =$

Moderate

Solution

$\begin{array}{l} \begin{array}{l} n (s) = 3^{5} \\ A \Rightarrow 4 Or more correct \\ \Rightarrow n (A) = 5 c_{4} \times 2 + 5 c_{5} = 5 \times 2 + 1 = 11 \\ P (A) = \frac{11}{3^{5}} = p \\ 3^{4} p = \frac{11}{3} = 3.67 \end{array} \end{array}$

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