Discrete probability distribution

 

An urn contains six red balls and seven green balls. One ball is drawn and its color noted. The ball is not replaced. Another ball is drawn and its color noted.

(a) Find the probability distribution of the number of red balls drawn.
(b) Confirm that the answer in (a) is a probability distribution.

This is sampling without replacement so use a tree diagram to enumerate the sample space.

Your tree diagram should look like this;

  

To find the probability for each value, multiply the probabilities along each branch.

With the probabilites added, your tree diagram should look like this:

  

Add probabilities for identical events. The branches RG and GR both produce a count of one R.

Your table should look like this:

  

Check the requirements for a probability distribution

All the probabilities are greater than or equal to zero.
The probabilities sum to 1

So the table does describe a probability distribution.

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

 

y

Now You Try:

Six cards have printed on them one each of the numbers from 1 to 6. The cards are arranged in a deck and one card is selected. It is recorded whether the number is odd or even. The card is not replaced in the deck. Another card is drawn and and it is recorded whether the number is odd or even.

(a) Find the probability distribution of the number of odd numbers drawn.
(b) Confirm that the answer in (a) is a probability distribution.