JEE Main · 2013 · 07 Apr 2013 · Offline · Probability

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A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

(A) $\frac{13}{3 ^{5}}$
(B) $\frac{11}{3 ^{5}}$ ✓ Correct
(C) $\frac{10}{3 ^{5}}$
(D) $\frac{17}{3 ^{5}}$

Answer: (B)

Solution

Guessing each of five questions right has probability

p = \frac{1}{3}

, and wrong

q = \frac{2}{3}

, and we want four or more correct. Exactly four:

(4 5) (\frac{1}{3})^{4} (\frac{2}{3}) = \frac{10}{243}

. Exactly five:

(\frac{1}{3})^{5} = \frac{1}{243}

. Together,

P (X \geq 4) = \frac{10 + 1}{243} = \frac{11}{3 ^{5}}

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

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