10. A student is taking a multiple choice test where each question have 5 possible answers of which only one is right. If the student knows the answer the student answers correctly, otherwise there is a 20% probability of correct answer. Assume the student knows 70% of the questions.

a. What is the probability of the student answering a question correct?

jkik

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To find the probability of the student answering a question correctly, we need to consider two scenarios: when the student knows the answer and when the student doesn't know the answer.

Let's denote:
P(K) = Probability that the student knows the answer (Given information: 70%)
P(N) = Probability that the student does not know the answer = 1 - P(K) = 1 - 0.70 = 0.30
P(C|K) = Probability of correct answer given that the student knows the answer = 100% = 1.00
P(C|N) = Probability of correct answer given that the student does not know the answer = 20% = 0.20

Now, to calculate the overall probability of the student answering a question correctly, we need to consider both scenarios:

P(C) = P(K) * P(C|K) + P(N) * P(C|N)
= 0.70 * 1.00 + 0.30 * 0.20
= 0.70 + 0.06
= 0.76

Therefore, the probability of the student answering a question correctly is 0.76 or 76%.