CONDITIONAL PROBABILITY

Designed by Engin A. Sungur

ACTIVITY

Suppose that you roll two fair dice. All possible outcomes of this experiment (which is called a sample space) is given in the following figure. Suppose that you see one of the dice and it shows 1. Given this information the possible outcomes of this experiment will change. To see the reduced sample space, move your cursor on the figure but do not click the mouse.


Define the following events

E = "the sum is 7"

F = "at least one of the dice shows a 1"

Note that

P(E)=6/36 and P(F)=11/36

If you see one of the dice and it shows 1, then the probability of sum being 7 changes to

P(E|F)=2/11=P(E and F)/P(F)=(2/36)/(11/36).

Do you think that seeing a 1 on one of the dice gives you a probabilistic information on the sum being equal to 7?

Yes No Do not know

EXTENSION

Suppose that you roll two fair dice with different colors (yellow and green). All possible outcomes of this experiment is given in the following figure. This time suppose that you see the yellow die and it shows 1. Given this information the possible outcomes of this experiment will change. To see the reduced sample space, move your cursor on the following figure but do not click the mouse.



Define the following events

E = "the sum is 7"

G = "yellow die shows a 1"

Note that

P(E)=6/36 and P(G)=6/36

If you see the yellow die and it shows 1, then the probability of sum being 7 changes to

P(E|G)=1/6=P(E and G)/P(G)=(1/36)/(6/36).

Do you think that seeing a 1 on the yellow die gives you a probabilistic information on the sum being equal to 7?

Yes No Do not know

ASSESSMENT

Briefly discuss the differences between the two cases, two same color dice and two different color dice. In your discussion refer to the concept of statistical independence.