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


one over six


two over six


three over six


four over six




07.01)Amanda created a table to help her represent the sample space of spinning a spinner and flipping a coin.





Result of spin


Result of coin toss Red Green Yellow Blue

Heads Red, heads Green, heads Yellow, heads Blue, heads

Tails Red, tails Green, tails Yellow, tails Blue tails



What is the probability that the result of the spin is blue and the coin lands heads up?


two over eight


three over eight


one over eight


four over eight





07.01)Kelly is picking out an outfit to wear. The organized list below represents the sample space of all possible outfits.


Red shirt – Black pants

Red shirt – White pants

Pink shirt – Black pants

Pink shirt – White pants


Based on the list, how many different-color shirts does Kelly have to choose from?


1


2


4


8




Which table correctly identifies the sample space of spinning the spinner and then selecting a card?


Results of the spin


Card Color Green Yellow Purple

Purple Green, Purple Yellow, Green Purple, Green

Green Green, Green Yellow, Yellow Purple, Red


Results of the spin


Card Color Green Yellow Purple

Purple Green, Purple Yellow, Purple Purple, Purple

Green Green, Green Yellow, Green Purple, Green


Results of the spin


Card Color Green Yellow Purple

Purple Green, Green Yellow, Yellow Purple, Red

Green Green, Purple Yellow, Green Purple, Green


Results of the spin


Card Color Green Yellow Purple

Purple Green, Purple Yellow, Purple Purple, Purple

Green Green, Green Yellow, Yellow Purple, Red


Based on the tree diagram, what is the probability that the art project is in the middle? one over six two over six three over six four over six 07.01)Amanda cr class=
Based on the tree diagram, what is the probability that the art project is in the middle? one over six two over six three over six four over six 07.01)Amanda cr class=

Verified Answer :

dalendrk

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.

View image dalendrk
View image dalendrk

------------- 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  


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