A multiple choice examination has 5 questions. Each… — JEE Main 2013 Mathematics PYQ

JEE Main 2013

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.
$\dfrac{17}{3^5}$
B.
$\dfrac{13}{3^5}$
C.
$\dfrac{11}{3^5}$
D.
$\dfrac{10}{3^5}$

Show answer and solution

Correct option: C

Solution

P(exactly 4 correct) = C(5,4)·(1/3)⁴·(2/3)¹ = 5·(1/81)·(2/3) = 10/243

P(exactly 5 correct) = C(5,5)·(1/3)⁵ = 1/243

Total = 10/243 + 1/243 = 11/243 = 11/3⁵

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