This is my first post - Hello
This question is quite long (but simple) so please bare with me...
"In a multiple-choice science test Geoff does not know the answer to questions 3 and 8. He has the choice of five answers (A, B, C, D or E) for each question. For question 8 he knows for certain that answers B and E are incorrect. He must guess from the rest of the answers. For questions 3 he must guess from all five of the answers. He is equally likely to choose any of the answers.
The correct answer to question 3 is E and for question 8 is it A. What is the probability that he gets:
a. Both questions correct.
b. Question 3 correct or questions 8 correct but not both correct.
c. At least one question correct "
I think I can answer a correctly:
P(8 AND 3 correct) = P(1/3) * P(1/5) = 1/15
But for b, I thought the working should be:
P(8 OR 3 correct) = P(1/3) + P(1/5) = P(5/15) + P(3/15) = 8/15
however the answer to b (in the book) is 2/5. Which suggests to me the book is workings is as follows:
P(3 OR 8 correct) = P(1/5) + P(1/5) = 2/5.
So my question is, why does the book use 1/5 as the probability of getting question 8 correct, when the statement says he knows for sure that B and E are incorrect (I guess this stems from the fact that I used the logic of 1/3 for question a)
Any pointers would be much appreciated.