Percent Mixture Probability

**sahip** · December 10th 2008, 04:58 PM

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 !

**Soroban** · December 10th 2008, 05:32 PM

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

**sahip** · December 11th 2008, 01:12 PM

Soroban,

Thank you for the solution. Well done !

sahip

Thread: Percent Mixture Probability

LinkBack

Thread Tools

Display

Percent Mixture Probability

Percent Mixture Probability

Similar Math Help Forum Discussions

percent mixture problem

probability with percent given.

Percent Mixture Need Help

percent mixture application extension

Percent mixture problems

Search Tags