Respuesta :
[tex] \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 }=\frac{8}{24}\\ \\ \text{now after first red ball drawn, there are total 23 balls out of which} [/tex]
[tex] \text{7 balls are red, so probability of drawing second red}=\frac{7}{23}\\ \\ \text{similarly probability of drawing 3rd red ball}=\frac{6}{22}\\ \text{probability of drawing fourth red ball}=\frac{5}{21}\\ \text{and probability of drawing fifth red ball}=\frac{4}{20} [/tex]
[tex] \text{so the probability of drawing 5 red balls}\\ \\ P(RRRRR)=\frac{8}{24}\times \frac{7}{23}\times\frac{6}{22}\times \frac{5}{21}\times \frac{4}{20}=\frac{1}{759}\\ \\ \text{similarly the probability of getting five white or five blue would be }\frac{1}{759}\\ \\ \text{hence the probability that all the balls are same color is}\\ \\ =\frac{1}{759}+\frac{1}{759}+\frac{1}{759}\\ \\ =\frac{3}{759}\\ \\ =0.0040 [/tex]
