Question

Based on the tree diagram, what is the probability that the art project is in the middle?

Answer 1

The explanation in the attachment.

Q1.
$\begin{array}{cccccc}science&-&art&-&math\\\dfrac{1}{3}&\times&\dfrac{1}{2}&\times&\dfrac{1}{1}&=\dfrac{1}{6}\end{array}\\------------------\\\begin{array}{cccccc}math&-&art&-&science\\\dfrac{1}{3}&\times&\dfrac{1}{2}&\times&\dfrac{1}{1}&=\dfrac{1}{6}\end{array}\\\\\\P(A)=\dfrac{1}{6}+\dfrac{1}{6}=\boxed{\dfrac{2}{6}}$

Answer: two over six

Q2.
$\begin{array}{cccccc}blue&-&head\\\dfrac{1}{4}&\times&\dfrac{1}{2}&=\dfrac{1}{8}\end{array}$

Answer: one over eight

Q3.
Answer: 2 - Red and Pink

Q4.
Answer : Second table /attachment/.

Card Color    Green                 Yellow                  Purple
                 Purple Green,    Purple Yellow,      Purple Purple,    Purple
                Green Green,      Green Yellow,      Green Purple,    Green

I don't know what happened to LaTeX. The formula of Q1 and Q2 in attachment.

Answer 2

------------- Solutions 

Part 1: $Science - Art - Math = Answer$ 

$Science = \frac{1}{3}$ 

$Art = \frac{1}{2}$ 

$Math = \frac{1}{1}$ 

$\frac{1}{3} * \frac{1}{2} * \frac{1}{1} = \frac{1}{6}$ 

$\frac{1}{3} * \frac{1}{2} * \frac{1}{1} = \frac{1}{6}$  

$P(A) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6}$ 

Part 2: $Blue - Head = Answer$ 

$Blue = \frac{1}{4}$ 

$Head = \frac{1}{2}$ 

$\frac{1}{4} * \frac{1}{2}$ 

$= 1 * 1 = 1 4 * 2 = 8$ 

$\frac{1}{4} * \frac{1}{2} = \frac{1}{8}$ 

Part 3: $Red + Pink$ 

Part 4: Card Color    Green                 Yellow                  Purple 
                 Purple Green,    Purple Yellow,      Purple Purple,    Purple 
                Green Green,      Green Yellow,      Green Purple,    Green