Probability with tree diagrams

Draw a tree diagram to help answer the question.
1.Steven and mansa toss a penny nickel and dime
a) what are the possible outcomes
b) steven gets a point if he tosses 2 or 3 heads while Mansa gets a point if he tosses 1 or 2 tails is it fair, if not, how can you change it to be fair

Hello, Luckygal!

Draw a tree diagram to help answer the question.
1. Steven and Mansa take turns tossing a penny, nickel and dime

a) What are the possible outcomes ?

Click to expand...

Steven has 8 possible outcomes.

. . \(\displaystyle \begin{array}{ccc} P & N & D \\ \hline
H&H&H \\ H&H&T \\ H&T&H \\ H&T&T \\
T&H&H \\ T&H&T \\ T&T&H \\ T&T&T \\ \hline \end{array}\)

And Mansa has the same possible outcomes.

b) Steven gets a point if he tosses 2 or 3 heads, while Mansa gets a point if he tosses 1 or 2 tails.
Is it fair? .If not, how can you change it to be fair?

Click to expand...

. . \(\displaystyle \begin{array}{ccccc}\text{Steven} &&&& \text{Mansa} \\
\text{wins} & P & N & D & \text{wins}\\ \hline
* & H&H&H \\ * & H&H&T & * \\ * & H&T&H & * \\ & H&T&T & * \\
* & T&H&H & * \\ &T&H&T & * \\ &T&T&H & * \\ & T&T&T \\ \hline \end{array}\)

\(\displaystyle \begin{array}{ccc}P(\text{Steven wins}) &=& \frac{4}{8} \:=\:\frac{1}{2} \\
P(\text{Mansa wins} &=& \frac{6}{8}\:=\:\frac{3}{4} \end{array}\)

The game is not fair.


To be fair:
. . Steven gets a point if he tosses 2 or 3 Heads.
. . Mansa gets a point if he tosses 2 or 3 Tails.


Then we have:

\(\displaystyle \begin{array}{ccccc}\text{Steven} &&&& \text{Mansa} \\
\text{wins} & P & N & D & \text{wins}\\ \hline
* & H&H&H \\ * & H&H&T \\ * & H&T&H \\ & H&T&T & * \\
* & T&H&H \\ &T&H&T & * \\ &T&T&H & * \\ & T&T&T & *\\ \hline \end{array}\)