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

Answer:

#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

Answer:

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 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