x Turn on thread page Beta
 You are Here: Home >< Maths

# Joint Probability watch

1. I am working on the following question:We choose numbers from {2; 3} by tossing a fair coin; the coin is tossed twice. Choose 2 if the coin turns up Heads and 3 if the coin is Tails. So the possible outcomes are {(2, 2), (2, 3), (3, 2), (3, 3)}. Let X be the first number chosen (so X is an element of {2, 3}) and let Y be the product of the two chosen numbers. Write down the joint distribution of X and Y as a table.My solution so far:This is my table for the joint probability:Table for probability of Y:Attachment 499007499009499000Table for probability of X:Attachment 499007499009499000

However there is a problem with the table for the probability of X. So I obtain the probabiity for each X = a by summing the rows in the joint probability table. But when I count the sample space it is different. In the cell (1,1) we have 1/4 but that cannot be right, it should be 1/2 because there are 2 events in the sample space that have the number 2 on first flip.

What is wrong?!

edit: something seems to be wrong uploaded the images for the last two tables. Click on the attachments!
Attached Images

2. (Original post by aspiring_doge)
I am working on the following question:We choose numbers from {2; 3} by tossing a fair coin; the coin is tossed twice. Choose 2 if the coin turns up Heads and 3 if the coin is Tails. So the possible outcomes are {(2, 2), (2, 3), (3, 2), (3, 3)}. Let X be the first number chosen (so X is an element of {2, 3}) and let Y be the product of the two chosen numbers. Write down the joint distribution of X and Y as a table.My solution so far:This is my table for the joint probability:Table for probability of Y:Attachment 499007499009499000Table for probability of X:Attachment 499007499009499000

However there is a problem with the table for the probability of X. So I obtain the probabiity for each X = a by summing the rows in the joint probability table. But when I count the sample space it is different. In the cell (1,1) we have 1/4 but that cannot be right, it should be 1/2 because there are 2 events in the sample space that have the number 2 on first flip.

What is wrong?!

edit: something seems to be wrong uploaded the images for the last two tables. Click on the attachments!
I'm not sure why you think that the probability for getting 2 on the first turn is 25%, it's 50% your table of outcomes is correct though. Just not your table for X values.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 30, 2016
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams