
There are 64 different possible outcomes, & in 9 of
these, exactly 2 of the balls will be red. There is thus a slightly better than
14% chance that exactly 2 balls will be red. A much faster way to solve the
problem is to look at it this way. There are 3 scenarios where exactly 3 balls
are red:
1 2 3
R R X
R X R
X R R
X is any ball that is not red. There is a 4.6875% chance that each of these
situations will occur. Take the first 1, for example: 25% chance the first ball
is red, multiplied by a 25% chance the second ball is red, multiplied by a 75%
chance the third ball is not red. Because there are 3 scenarios where
this outcome occurs, you multiply the 4.6875% chance of any 1 occurring by 3,
& you get 14.0625%.
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