Yellow White Two
Probability of drawing less than two yellow marbles?

A bag contains 8 red marbles, 8 blue marbles, 10 white marbles and 8 yellow marbles. You are asked to draw 5 marbles from the bag without replacement. What is the probability drawing less than two yellow marbles?

There are 8 yellow marbles and 26 which are not yellow, a total of 34.

Probability of drawing less than 2 yellows
= probability of drawing 0 OR 1 yellow
= probability of drawing 0 yellows + probability of drawing 1 yellow.

Probability of drawing 5 marbles which are not yellow:

P(0)= (26x25x24x23x22)/(34x33x32x31x30)

Probability of drawing 1 yellow followed by 4 which are not yellow:

P(1)= (8/34)x(26x25x24x23)/(33x32x31x30)

The yellow can be drawn on 1st, 2nd, 3rd, 4th or 5th turn, so this probability must be multiplied by 5.

So the total probability is

P(0,1) = (5x8+22)x(26x25x24x23)/(34x33x32x31x30) = 0.6662.

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