a multiple choice test consists of 8 question with 3 answers of each question. A student answers each question by rolling q dice and checking the first answer if he gets 1 or 2 then second answer 3or 4 and third if he gets 5 or 6.to get a distinction he must secure atleast 75% correct answer. if there is no negative marking what is the probability that student secures distinction
Answers
Given : a multiple choice test consists of 8 question with 3 answers of each question
A student answers each question by rolling a dice
first answer if he gets 1 or 2
second answer 3 or 4
third if he gets 5 or 6.
.to get a distinction he must secure atleast 75% correct answer
To find : what is the probability that student secures distinction
Solution:
Probability of Each correct answer p = 2/6 = 1/3
Probability of incorrect answer = q = 1 - 1/3 = 2/3
n = 8
P(x) = ⁿCₓpˣqⁿ⁻ˣ
atleast 75% correct answer
=> (75/100)8 = 6
Correct answers = 6 , 7 or 8
probability that student secures distinction = P(6) + P(7) + P(8)
= ⁸C₆(1/3)⁶(2/3)² + ⁸C₇(1/3)⁷(2/3)¹ + ⁸C₈(1/3)⁸(2/3)⁰
= 28 * 4 / 3⁸ + 8 * 2 / 3⁸ + 1/3⁸
= 112/6561 + 16/6561 + 1/6561
= 129/6561
= 43/2187
= 0.01966
probability that student secures distinction = 43/2187 or 0.01966
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Answer:
A multiple choice test contains 8 questions with 3 answers to each question (of which one is only correct). A student answers each question by rolling a balanced dice and checking the first answer if he gets 1 or 2, the second answer if he gets 3 or 4, and third answer if he gets 5or 6. To get a distinction the students must secured at least 75 percentage correct answers. If there is no negative marking, what is the probability that the students get distinction