Question

The probability that a student correctly answers on the first try (the event A) is P(A) = 0.3. 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 0.4. Find the probability that the student answers the question on the first or second try.

a) 0.88

b) 0.12

c) 0.70

d) 0.42

e) 0.58

Answer 1

P( correctly answers on the first try) = P(A) = 0.3

P( incorrectly answers on the first try ) = P( not A ) =1 - ( correctly answers on the first try )

P( incorrectly answers on the first try ) = P( not A ) = 1- 0.3

P( incorrectly answers on the first try ) = P( not A ) = 0.7

P[ the student answers correctly on the second try given that he answered incorrectly on the first try ] = P[ B | not A ] = 0.4

P[ the student answers correctly on the second try and did not answer on first try ] = P[ B and not A ] = P[ B | not A ]*P( not A )

P[ the student answers correctly on the second try and did not answer on first try ] = P[ B and not A ] = 0.7*0.4 = 0.28

We need to find

P[ the student answers the question on the first or second try ] = P[ B and not A ] + P[ A ]

P[ the student answers the question on the first or second try ] = 0.28 + 0.3

P[ the student answers the question on the first or second try ] = 0.58