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Math Help - Percent Mixture Probability

  1. #1
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    Smile Percent Mixture Probability

    A website sells 3 types of chocolate bars of equal weight. If John orders 2 chocolate bars at random from the website, then melts them together, what is the probability that the resulting mix contains at least 50% cocoa by weight ?

    Type % Cocoa by weight
    Milk 35
    Dark 50
    Bittersweet 70

    Thank you !
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  2. #2
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    Hello, sahip

    A website sells 3 types of chocolate bars of equal weight.
    If John orders 2 chocolate bars at random from the website, then melts them together,
    what is the probability that the resulting mix contains at least 50% cocoa by weight ?

    . . \begin{array}{ccc}\text{Type} & & \text{\% Cocoa} \\ \hline<br />
\text{Milk} & & 35 \\ \text{Dark} & & 50 \\ \text{Bittersweet} & & 70 \end{array}

    There are six equally likely outcomes: .MM, MD, MB, DD, DB, BB


    The cocoa content is given by:

    . . \begin{array}{ccc} & & \text{\% cocoa} \\<br />
\text{Types} & & \text{in mixture} \\ \hline MM & & 35 \\ MB & & 42.5 \\ MB & & 52.5 \\ DD & & 50 \\ DB & & 60 \\ BB & & 70 \end{array} \begin{array}{c}{\color{white}.}\\ {\color{white}.}\\ {\color{white}.}\\ {\color{white}.} \\ \\[-2mm] \Leftarrow \\ \Leftarrow \\ \Leftarrow \\ \Leftarrow \end{array}


    Therefore: . P(\text{cocoa} \geq 50\%) \;=\;\frac{4}{6} \;=\;\frac{2}{3}

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  3. #3
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    Smile Percent Mixture Probability

    Soroban,

    Thank you for the solution. Well done !

    sahip
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