A multiple choice test consist of 8 questions with 3 answer to each question
(of which only one is correct). A student answers each question by rolling a
balanced dice & checking the first answer if he gets 1 or 2, the second answer
if he gets 3 or 4 & the third answer if he gets 5 or 6. To get a distinction, the
student must secure at least 75% correct answers. If there is no negative
marking, what is the probability that the student secures a 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
Learn More :
The probability of a component's failure is 0.05. Out of 14 ...
brainly.in/question/19727623
If probability is 0.55 that a person will believe in a piece of fake news ...
brainly.in/question/19591686
Human error is given as the reason for 75% of all accidents in a ...
brainly.in/question/16832177