A box contains one yellow two red and three green balls Two

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events:

A:{ One of the balls is yellow }
B:{ At least one ball is red }
C:{ Both balls are green }
D:{ Both balls are of the same color }

P(B|Ac) =

P(B|Dc)

Solution

1y
2r
3G

A)

P(B|Ac) = the probability of at least one ball is red, given that none of them is yelow

There are 5C2 = 10 ways to choose 2 non-yellow items.

Note that

P(at least one red) = 1 - P(no red).

Thus, there are 3C2 = 3 ways to get non-red balls.

Thus,

P(no red) = 3/10 = 0.3

Thus,

P(B|Ac) = P(at least one red) = 1 - 0.3 = 0.7 [ANSWER]

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B)

P(B|Dc) = the probability of at least one ball is red, given that the balls don\'t have the same color.

There are

1*2 = 2 ways to get yellow and red
1*3 = 3 ways to get yellow and green
2*3 = 6 ways to get red and green

A total of 11 ways, of which, 2+6 = 8 have a red.

Thus,

P(B|Dc) = 8/11 = 0.727273 [answer]