The probability that the question is hard is 0.85. Find the Probability of answering a question correctly.

nicekikah

nicekikah

Answered question

2021-09-17

If a question is hard, you can answer it correctly with probability 0.01. If the question is easy, you can answer it correctly with probability 0.9. The probability that the question is hard is 0.85. Find the Probability of answering a question correctly. a. 0.3964 b. 0.1435 c. 0.8356 d. 0.7732 e. 0.2564

Answer & Explanation

timbalemX

timbalemX

Skilled2021-09-18Added 108 answers

Given: There are a total of 10 questions.
Probability of answering a hard question correctly=0.01
Probability of answering an easy question correctly=0.9
The probability that the question is hard=0.85
So, the probability that the question is easy=1−0.850.15
The probability that the question is answered correctly=
(Probability that the question is hard × Probability of answering the hard question correctly)+(Probability that the question is easy × Probability of answering the easy question correctly)
Thus, the desired probability is:
P(answered correctly)=P(hard ques)×P(hard ques answered correclty)+P(easy ques)×P(easy ques answered correclty)0.85×0.01+0.15×0.90.0085+0.1350.1435
Thus, the probability of answering a question correctly is 0.1435.
Hence, option b. 0.1435 is correct.

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