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4 February, 13:54

Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?

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  1. 4 February, 14:28
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    If you wanna estimate the probability of an event to happen, you have to multiply the probability of success of all the situations involved.

    - Probability to get the first sweatshirt made of cotton: 7 of 16.

    - Probability for the second one: 6 of 15, because there's one shirt less, and one cotton less.

    - Prob for the third: 5 of 14

    - Prob for the fourth: 4 of 13

    So the probability to get four cotton shirts is: 7/16·6/15·5/14·4/13 = 0'019, something that could be rounded to 2%.
  2. 4 February, 15:51
    0
    There are 16 sweatshirts in total.

    7 of which are cotton.

    There are 4 friends.

    Say they all choose cotton sweatshirts,

    First friend: (7/16)

    Second friend: (6/15)

    Third friend: (5/14)

    Fourth friend: (4/13)

    As you can see, there is a deduction in total number of sweatshirts available to be chosen and also in the total number of cotton sweatshirts available to be chosen.

    Multiply these together = (7/16) * (6/15) * (5/14) * (4/13)

    = 0.01923076923 = 1.92%

    1.92% is the probability all friends order cotton sweatshirts
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