Given:
Percent of participants that used triangles shape = 80% = 0.80
The triangles shaped won their trials 16% of the time = 0.16
The other shaped plane won their trials 36% of the time = 0.36
Thus, we have:
Percent of participants who used other shapes = 100% - 80% = 20% = 0.20
Amount of time the triangle shaped plane lost = 100% - 16% =84% = 0.84
Amount of time the other shaped plane lost = 100% - 36% = 64% = 0.64
Let's solve for the following:
• (a) Create a tree diagram for this situation.
We have the tree diagram below:
• (b) What is the probability that a triangle plane won overall?
To find the probability that a triangle plane won overall, we have:
[tex]P(\text{triangle)}=\frac{0.8\times0.16}{(0.8\times0.16)+(0.2\times0.36)}=\frac{0.128}{0.128+0.072}=0.64[/tex]• (c) Out of 100 planes, which shape has the most winners?
Given that 80% used triangle, the number of planes with triangle shape will be:
0.8 x 100 = 80 planes
Number of planes with other shape:
0.2 x 100 = 20 planes
Number of winners for traingles:
0.16 x 80 = 12.8
Number of winners for other shape:
0.36 x 20 = 7.2
Therefore, the shape with the most winners is the triangle shape.
• (d),. A winning plane is selected at random, what is the chance it is triangle shaped?
To find the probability a winning plane selected at random is triangle shaped, wehave:
[tex]P(\text{triangle)}=\frac{12.8}{12.8+7.2}=\frac{12.8}{20}=0.64[/tex]ANSWER:
(b) 0.64
(c) Triangle shape
(d) 0.64
