# Balls in bags, 4 answers to 4 exam questions.

• Sep 30th 2010, 09:50 PM
juliak
I am unsure of how to solve these questions:

2. A bag contains 3 red balls and one blue ball. A second bag contains one red ball and one blue ball. A ball is picked out of each bag and is then placed in the other bag. What is the expected number of red balls in the first bag?

I am not sure how to set up a tree diagram to solve this question.

3. In an examination a candidate is given the four answers to four questions but is not told which answer applies to which question. He is asked to write down each of the four answers next to its appropriate question.

a). Calculate in how many different ways he could write down the four answers.
I don't even know how to do a. I thought the answer was 16 because 4*4 but the answer is actually 24.. :S How do I do this?

b). Explain why it is impossible for him to have just 3 answer in the correct places and show that there are 6 ways of getting just two answers in the correct places.

c). If a candidate guesses at random where the four answers are to go and X is the number of correct guesses he makes, draw up the probability distribution for X in tabular form.
• Oct 1st 2010, 05:15 AM
mr fantastic
Quote:

Originally Posted by juliak
I am unsure of how to solve these questions:

2. A bag contains 3 red balls and one blue ball. A second bag contains one red ball and one blue ball. A ball is picked out of each bag and is then placed in the other bag. What is the expected number of red balls in the first bag?

I am not sure how to set up a tree diagram to solve this question.

3. In an examination a candidate is given the four answers to four questions but is not told which answer applies to which question. He is asked to write down each of the four answers next to its appropriate question.

a). Calculate in how many different ways he could write down the four answers.
I don't even know how to do a. I thought the answer was 16 because 4*4 but the answer is actually 24.. :S How do I do this?

b). Explain why it is impossible for him to have just 3 answer in the correct places and show that there are 6 ways of getting just two answers in the correct places.

c). If a candidate guesses at random where the four answers are to go and X is the number of correct guesses he makes, draw up the probability distribution for X in tabular form.

2) The possible outcomes for bag 1 are 4R, 3R 1B and 2R 2B. Calculate the probability of each and use those probabilities to calculate the expected number of R.

3a). Google derangement. Mr F edit: This is not relevant to the question.

b) and c). What thoughts have you had? Where are you stuck? Part c) can be linked to a) and b) ....
• Oct 1st 2010, 01:10 PM
awkward
I don't follow Mr. F's answer to 3a-- I think we must interpret the question differently? Anyway, according to my interpretation, the correct answer is indeed 24.

That is because the number of possible orderings of the 4 answers is 4!.
• Oct 1st 2010, 01:41 PM
mr fantastic
Quote:

Originally Posted by awkward
I don't follow Mr. F's answer to 3a-- I think we must interpret the question differently? Anyway, according to my interpretation, the correct answer is indeed 24.

That is because the number of possible orderings of the 4 answers is 4!.

Quite right. My mistake.
• Oct 1st 2010, 01:51 PM