Answer:
0.08475
Step-by-step explanation:
The question above is a application of conditional probability.
The formula to use is Baye's Theorem for conditional probability.
From the above question we have the following information:
Probability of answering correctly when prepared = 0.9
Probability of not answering correctly when prepared = 1 - 0.9 = 0.1
Probability of choosing the right answer = 1/4 = 0.25
Probability of choosing the wrong answer = 1 - 0.25 = 0.75
Number of students that prepare for the quiz = 75% = 0.75
Therefore number of students that did not prepare for the quiz = 1 - 0.75
= 0.25
Hence,
The probability of not preparing but choosing the correct answer =
P[ not prepared | correct answer ]
Is calculated as :
P[ not prepared | correct answer ] =
(0.25 × 0.25)/(0.25 × 0.25) + (0.25 × 0.9)
= 0.08475
Therefore, the chance that Mr X did not prepare for the quiz but he gives the right answer = 0.08475
