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# A test has 5 multiple-choice questions. Each question has 4 answer opt

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Intern
Joined: 28 Jan 2017
Posts: 26
A test has 5 multiple-choice questions. Each question has 4 answer opt  [#permalink]

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09 Jan 2020, 18:42
3
00:00

Difficulty:

75% (hard)

Question Stats:

36% (02:57) correct 64% (02:12) wrong based on 14 sessions

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A test has 5 multiple-choice questions. Each question has 4 answer options (A,B,C,D). What is the probability that a student will choose “B” for at least four questions if no questions are left blank?

A) 1/256
B) 5/1024
C) 1/64
D) 21/1024
E) 1/16
CrackVerbal Quant Expert
Joined: 12 Apr 2019
Posts: 385
Re: A test has 5 multiple-choice questions. Each question has 4 answer opt  [#permalink]

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10 Jan 2020, 01:31
In this question on probability, we need to understand two things:
#1 – Any of the four/five questions can have the answer as B, so we need to select those four/five questions.
#2 – The probability of getting B as the right answer is ¼ and that of not getting B as the right answer is ¾.

The number of ways of selecting any 4 questions of 5 = $$5_C_4$$ = 5. In each of these 5 cases, the probability that the student will choose B as an answer is ¼ and the probability that he will not choose B is ¾.
Therefore, probability that the student will choose B for 4 questions = 5 * $$(\frac{1}{4})^4$$ * ($$\frac{3}{4}$$) = $$\frac{15 }{ 1024}$$.

The number of ways of selecting all 5 questions of 5 = $$5_C_5$$ = 1.
Therefore, probability that the student will choose B for all 5 questions = 1 * $$(\frac{1}{4})^5$$ * $$(\frac{3}{4})^0$$ = $$\frac{1 }{ 1024}$$.

The total probability =$$\frac{15 }{ 1024}$$ + $$\frac{1 }{ 1024}$$ = $$\frac{16 }{ 1024}$$ = $$\frac{1 }{ 64}$$.
The correct answer option is C.

Hope that helps!
_________________
Re: A test has 5 multiple-choice questions. Each question has 4 answer opt   [#permalink] 10 Jan 2020, 01:31
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