An objective type test paper has 5 questions. Out of these 5 questions, 3 questions have four options each (A, B, C, D) with one option being the correct answer. The other 2 questions have two options each, namely True and False. A candidate randomly ticks the options. Then the probability that he/she will tick the correct option in at least four questions, is

Question

An objective type test paper has 5 questions. Out of these 5 questions, 3 questions have four options each (A, B, C, D) with one option being the correct answer. The other 2 questions have two options each, namely True and False. A candidate randomly ticks the options. Then the probability that he/she will tick the correct option in at least four questions, is (A) (5/32) (B) (3/128) (C) (3/256) (D) (3/64)

Tardigrade Admin · Accepted Answer

Total sample space, n(S)=43 ⋅ 22 and total number of favourable cases n(E) =( 3 C1 ⋅ 3+ 2 C1 ⋅ 1)+1 Required probability = (n(E)/n(S)) = ( 3 C4 ⋅ 3+ 2 C1 ⋅ 1+1/43 ⋅ 22)=(3 ⋅ 3+2+1/43 ⋅ 4) =(12/64 ⋅ 4)=(3/64)

$\frac{5}{32}$

$\frac{3}{128}$

$\frac{3}{256}$

$\frac{3}{64}$

325​

1283​

2563​

643​

Total sample space, n(S)=43⋅22 and total number of favourable cases n(E)=(3C1​⋅3+2C1​⋅1)+1 Required probability =n(S)n(E)​ =43⋅223C4​⋅3+2C1​⋅1+1​=43⋅43⋅3+2+1​ =64⋅412​=643​

$\frac{5}{32}$

$\frac{3}{128}$

$\frac{3}{256}$

$\frac{3}{64}$