# Math Help - Percent Mixture Probability

1. ## 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 !

2. 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 ?

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

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

The cocoa content is given by:

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

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

3. ## Percent Mixture Probability

Soroban,

Thank you for the solution. Well done !

sahip