Assume that the box contains 11 balls: 4 red, 5 blue, and 2 yellow. As in the text, you draw one ball, note its color, and if it is yellow replace it. If it is not yellow you do not replace it. You then draw a second ball and note its color.
(2) What is the probability that the second ball drawn is red?
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There are 2 cases
the first ball drawn is red
the first ball drawn is not red
there are 4 red balls and 22 balls in total
the chance you are in case 1 is
change you are in case 2 is
when you are in case 1
you have a 3/21 chance of picking up a red ball the 2nd time
when you are in case 2
you have a 4/21 chance of picking up a red ball the 2nd time
Total prob of picking up a red is therefore
4/22*3/21 + 18/22*4/21
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another way to view this problem is you are solvint these 2 cases
(2) There is a 2/11 probability of the first ball being yellow, in which case there
would be a 4/11probability of the second ball being red.
There is a 4/11 probability of the first ball being red, in which case there is a
3/10 chance of the second ball being red.
There is a 5/11 probability of the first ball being blue, in which case there is a
4/10 probability of the second ball being red.
So the probability that the second ball drawn is red is
(2/11)(4/11) + (4/11)(3/10) + (5/11)(4/10) =