I am working my way through an example problem from Goldberg's "Probability: An Introduction".
There are x red balls and x green balls in an urn. Total number of balls in the urn is 5. You must guess the colour of the ball being drawn by Mr Y using a number of strategies. I am having problems with strategies 4 and 5:
Draw a ball from the urn and replace it. Then draw another ball and replace it. If both balls are red, then guess Y will draw a red ball. If both balls are green then guess Y will draw a green ball. If you draw one red and one green ball, then draw one more ball from the urn. If this ball is red, then guess Y will draw a red ball. If it is green, then guess Y will draw a green ball.
Same as strategy 4, except that the first ball is not replaced before the second is drawn. Also, if a third ball is required, it is done without replacing the first two balls.
The example suggests drawing a table with the strategies as columns and the number of red balls as rows. The cells contain the probability of guessing a red ball given the number of red balls in the urn. My problem is with strategy 5 where you have just one red ball in the urn.
You have 1/5 probability of obtaining the red ball in the first draw. Let's say it is obtained, then, because it is not replaced, there is 0 probability of obtaining the red ball in the second draw. This means that the probability of obtaining a red ball is 0 for all cases where there is only one red ball and you draw it first up. If that is right, then it also means that there is 0 probability of guessing the red ball if you guess green then red, or red then green. Am I on the right track? The answer is a probability of 0.8 for 1 red ball in the urn for strategy 5, but this is not what I am getting.
Thanks in advance for any tips or help.