They gave a test of 22 multiple-choice questions. Each question

Dalia Morales

Dalia Morales

Answered question

2022-02-11

They gave a test of 22 multiple-choice questions. Each question has 4 possible answers, only one of which is correct. What is the probability that you will guess at most three correctly?

Answer & Explanation

lofia1r

lofia1r

Beginner2022-02-12Added 15 answers

Step 1
Each question has 4 possible answers only one of which is correct, if I do not have the knowledge or aware about the answer and we depend upon guess, the probability of getting that particular answer right is 14
However, there are 22 question each of which has a probability of being correctly answered is 14, the probability of exactly r of them being answered correctly P(r) is given by
P(r)=xnCrprq(nr), where q=1p
Further, as we desire the guessing of at most 3 answers correctly i.e. P(r3), this is
P(r3)=P(0)+P(1)+P(2)+P(3)
=22C0(14)0(34)22+22C0(14)1(34)21+22C0(14)2(34)20+22C0(14)3(34)19
=(34)22+22×14×(34)21+22×211×2×(14)2×(34)20+22×21×201×2×3×(14)3×(34)19
=0.00178381+0.01308125+0.04578437+0.10174305
=0.16239248
Hence, the probability that you will guess at most 3 answers correctly is 0.1624

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