Question

Refer to example 4.40. an urn contains eight red balls, eight white balls, and eight blue balls, and sample of five balls is drawn at random without replacement. compute the probability that all of the balls in the sample are the same color. (round your answer to four decimal places.) 0.0009 incorrect: your answer is incorrect.

Answer 1

`\text{An urn contains eight red balls, eight white balls and eight blue balls.}\\ \text{so there are total 24 balls in urn.}\\ \\ \text{now a sample of five balls is drawn at rendom without replacement.}\\ \\ \text{So in order to get all the balls of same colour we have:}\\ \\ \text{for red ball, the probability of drawing firt ball }=(8)/(24)\\ \\ \text{now after first red ball drawn, there are total 23 balls out of which}`

`\text{7 balls are red, so probability of drawing second red}=(7)/(23)\\ \\ \text{similarly probability of drawing 3rd red ball}=(6)/(22)\\ \text{probability of drawing fourth red ball}=(5)/(21)\\ \text{and probability of drawing fifth red ball}=(4)/(20)`

`\text{so the probability of drawing 5 red balls}\\ \\ P(RRRRR)=(8)/(24)* (7)/(23)*(6)/(22)* (5)/(21)* (4)/(20)=(1)/(759)\\ \\ \text{similarly the probability of getting five white or five blue would be }(1)/(759)\\ \\ \text{hence the probability that all the balls are same color is}\\ \\ =(1)/(759)+(1)/(759)+(1)/(759)\\ \\ =(3)/(759)\\ \\ =0.0040`