Question

A bag contains 3 red marbles, 5 yellow marbles and 6 orange marbles. Three marbles are drawn and NOT replaced each time. Determine the probability of drawing three yellow marbles in a row. State whether the events are dependent or independent.

Answer 1

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

First marble = 5/14

With one less yellow marble, second = 4/13

With another less yellow marble, third = ?

Multiply the three values.

Answer 2

I'm still not sure.. I'm good with independent events but these dependent one has me confused..

Answer 3

I think I solved it:

RRR,YYYYY,OOOOOO

[RYO],[RRR],[RYY],[ROO]
[YYY],[YOR],[YOO],[YYO],[YRY],[YRR]
[OOO],[ORO],[OYO],[ORR],[OYY],[ORY]

There are 16 probable outcomes, only one of which was favourable, so 1/16=0.0625 so there is a 6% probability of you drawing 3 yellows!

This event is dependent as the probability of drawing another yellow marble can either reduce or increase depending on the amount of each colour that remains inside the bag.