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 Four balls (Posted on 2017-05-19)
There are four balls in a hat: a blue one, a white one, and two red ones. Now I draw simultaneously two balls, look at them, and announce that at least one of them is red.

What is the chance that the other is red as well?

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 Solution | Comment 3 of 22 |
There are 6 different ways to pick a pair of balls from a set of four.  The number of red balls in a pair varies among the six different ways.

One way has zero red balls (blue+white).  In this event Ady cannot declare there is at least one red ball.
Four ways have one red ball (red#1+blue, red#2+blue, red#1+white, red#2+white).  In these events Ady can declare there is at least one red ball.
One way has two red balls (red#1+red#2). In this event Ady can declare there is at least one red ball.

Out of the six possible draws, only five of them can Ady make his statement.  Out of those five, only one has both red balls, therefore the chance that the other is red as well is 1/5.

 Posted by Brian Smith on 2017-05-19 12:43:07

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