An urn contains 100 marbles: 20 white, 30 red, 50 green. Calculate the probability of selecting White, Red and Green marbles respectively. What is the probability of pulling a white, green, white and red marbles consecutively?

2 Answers
Apr 18, 2016

950/156849 or approximately 0.6%

Explanation:

Assuming the marbles are not replaced in the urn:

  • The probability of the first marble being white is 20/100

  • The probability of the next marble being green is then 50/99

  • The probability of the next marble being white is 19/98

  • The probability of the next marble being red is 30/97

So the probability of the sequence white, green, white, red is:

20/100 * 50/99 * 19/98 * 30/97

=10/color(red)(cancel(color(black)(50)))*color(red)(cancel(color(black)(50)))/99*19/98*30/97

=(10*19*30)/(99*98*97)

=(color(red)(cancel(color(black)(3)))*1900)/(color(red)(cancel(color(black)(3)))*33*98*97)

=1900/(33*98*97)

=(color(red)(cancel(color(black)(2)))*950)/(33*color(red)(cancel(color(black)(2)))*49*97)

=950/(33*49*97)

=950/156849 ~~ 0.006

That is approximately 0.6%

Aug 24, 2016

In support of Georg's solution

Explanation:

For probability questions of this type, if you are ever in doubt, draw a probability tree

color(red)("Assumption: this is selection without replacement")

From the diagram observe that the initial selection of
White ->20/100->20%

Red" "-> 30/100->30%

Green->50/100->50%

Tony BTony B

From the probability tree the overall sequenced sampling probability of white: green: white: red is:

20/100xx50/99xx19/98xx30/97

For what follows refer to George's solution