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.

Important This is not a 'textbook on a screen' - this is an interactive learning system. Which means you have to 'act' to make it go.

Look through the options below and select the one you think is the best response. You will gain most benefit if you work the problem with pen and paper as you go, i.e. decide what you think is the correct option and write down what you think the result will be before you click. If the next step doesn't display, click another option.

 

How would you enumerate the elements of the sample space?

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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.

 

Count the elements of the sample space
Use a tree diagram
Make a list