Probability of drawing less than two yellow marbles?

December 19th, 2009 | by admin |

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)= (26×25x24×23x22)/(34×33x32×31x30)

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

P(1)= (8/34)x(26×25x24×23)/(33×32x31×30)

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) = (5×8+22)x(26×25x24×23)/(34×33x32×31x30) = 0.6662.

  1. 4 Responses to “Probability of drawing less than two yellow marbles?”

  2. By miryana kina on Dec 19, 2009 | Reply

    answer
    = [8C1 * 26C4 + 8C0 * 26C5] / 34C5
    = [8 * 14950 + 1 * 65780] / 278256
    = 185380 / 278256
    = 0.666221
    References :

  3. By Brittanyy(: on Dec 19, 2009 | Reply

    do your own homework(:
    References :

  4. By Kristofer B on Dec 19, 2009 | Reply

    8+8+8+10=34 less than 2 is one, so 8/34=23.5%
    References :

  5. By Barry G on Dec 19, 2009 | Reply

    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)= (26×25x24×23x22)/(34×33x32×31x30)

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

    P(1)= (8/34)x(26×25x24×23)/(33×32x31×30)

    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) = (5×8+22)x(26×25x24×23)/(34×33x32×31x30) = 0.6662.
    References :

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