Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 months ago

A company produces boxes of sweets that contain 5 jellies and 3 chocolates. Jemeel crosses 3 sweets at random from a box?

Draw up the probability distribution table for the number of jellies that Jemeel chosses.

on the mark scheme

p(1)=5/8 X 3/7 X 2/6 X3= 15/56

P(2)= 5/8 X 4/7 X 3/6 X3=30/56

I don't understand why we have to multiply by 3

1 Answer

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  • 3 months ago

    He can choose 1 jelly sweet in 3 ways as he can choose it 1st, 2nd or 3rd.

    So, choosing jelly first we have:

    5/8 x 3/7 x 2/6

    Choosing a jelly either 2nd or 3rd give the same calculation

    Hence, P(1 jelly) = 3 x (5/8 x 3/7 x 2/6) = 15/56

    Choosing 2 jellies, we have either (J,J,C) or (J,C,J) or (C,J,J)...i.e. 3 ways

    Now, J,J,C => 5/8 x 4/7 x 3/6 = 5/28

    Multiplying by 3 gives 15/28 => 30/56

    Finally, choosing 3 jellies can only happen in 1 way

    i.e. 5/8 x 4/7 x 3/6 => 5/28 = 10/56

    Let's not forget that he can pick no jellies, i.e. all chocs

    so, 3/8 x 2/7 x 1/6 = 1/56 

    In summary, we have,

    P(0) = 1/56

    P(1) = 15/56

    P(2) = 30/56

    P(3) = 10/56

    Check: total 56/56 = 1

    :)>

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