The probability that a student correctly answers on the first try (the event A)

Question

The probability that a student correctly answers on the first try (the event A) is P(A) 0.2. If the student answers incorrectly on the first try, the student is allowed a second try to correctly answer the question (the event B). The probability that the student answers correctly on the second try given that he answered incorrectly on the first try is 0.3. Find the probability that the student correctly answers the question on the first or second try. a) 0.44 b 0.50 c 0.06 0.36 0.41 None of the above.

Explanation / Answer

Ans:

P(correct at first try)=P(A)=0.2

P(incorrect at first try)=P(A')=0.8

P(correct at second try)=P(B)

P(correct at second try/incorrect at first try)=P(B/A')=0.3

So,

P(B/A')=P(B and A')/P(A')

P(B and A')=0.3*0.8=0.24

Then,

P(correctly answer on first or second try)=P(A)+P(B and A')=0.2+0.24=0.44

Option a is correct(0.44)

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