Abox contains one yellow, two red, and three green balls. two balls are randomly chosen without replacement. define the following events: : { one of the balls is yellow } : { at least one ball is red } : { both balls are green } : { both balls are of the same color }. find the following conditional probabilities: (a) p(bia) (b) p(dib) (c) p(cid)

Answer and explanation:

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

To find : Define the following events and the following conditional probabilities ?

Solution :

Number of yellow balls = 1

Number of red balls = 2

Number of green balls = 3

Let A be the event that 'One of the balls is yellow'

So,

Let B be the event that 'At least one ball is red'

So,

Let C be the event that 'Both balls are green'

So,

Let D be the event that 'Both balls are of the same color'

So,

Conditional probabilities,

a)

means one ball is yellow and one is red,

b)

means both ball are red,

c)

means both ball are green,

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