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
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
In support of Georg's solution
Explanation:
For probability questions of this type, if you are ever in doubt, draw a probability tree
From the diagram observe that the initial selection of
From the probability tree the overall sequenced sampling probability of white: green: white: red is:
For what follows refer to George's solution