Missing steps in probability question.

Hi,

This is my first post - Hello (Happy)

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.

Thanks

Re: Missing steps in probability question.

Quote:

Originally Posted by

**cp3o** *"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.

c. Question 3 correct or questions 8 correct but not both correct.

d. 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.

Well I disagree with both you and the textbook.

$\displaystyle P(\text{8 or 3})=P(8)+P(3)-P(\text{8 and 3})=\frac{1}{3}+\frac{1}{5}-\frac{1}{15}$

Re: Missing steps in probability question.

Quote:

Originally Posted by

**Plato** Well I disagree with both you and the textbook.

$\displaystyle P(\text{8 or 3})=P(8)+P(3)-P(\text{8 and 3})=\frac{1}{3}+\frac{1}{5}-\frac{1}{15}$

Thanks for the reply. Could you explain why you did it that way? I thought mutually exclusive events are P(A or B) = P(A) + P(B). Wouldn't your answer be correct for question d (at least one correct)?

Re: Missing steps in probability question.

Quote:

Originally Posted by

**cp3o** I thought mutually exclusive events are P(A or B) = P(A) + P(B). Wouldn't your answer be correct for question d (at least one correct)?

First you explain why think they are **mutually exclusive events**.

If they were then $\displaystyle P(\text{8 and 3})=0$.

Re: Missing steps in probability question.

I think they are mutually exclusive by the way the question is worded... Question 3 correct OR questions 8 correct but not both correct. So P(3 or 8)?

Plato,

Apologies if I am frustrating you, I am trying (although I know I can be!)

Re: Missing steps in probability question.

Quote:

Originally Posted by

**cp3o** I think they are mutually exclusive by the way the question is worded... Question 3 correct OR questions 8 correct but not both correct. So P(3 or 8)?

Events are *mutually exclusive*, if they cannot occur at the same time.

Can he answer both #3 & #8 correctly at the same time?

If so then that are not mutually exclusive.

This is a very very basic fact of probability:

$\displaystyle P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $\displaystyle \cup\text{ means OR}$ and $\displaystyle \cap\text{ means AND}$.