Question

A paper airplane contest is being held. The following results are found: 80% of the participants used a triangle shape. The triangle shaped planes only won their trials 16% of the time. The other shaped planes won their trials 36% of the time. Create a tree diagram for this situation: What is the probability that a triangle plane won overall?Out of 100 planes, which shape has the most winners?A winning plane is selected at random, what is the chance it is triangle shaped?

Answer 1

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:

`P(\text{triangle)}=(0.8*0.16)/((0.8*0.16)+(0.2*0.36))=(0.128)/(0.128+0.072)=0.64`

• (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:

`P(\text{triangle)}=(12.8)/(12.8+7.2)=(12.8)/(20)=0.64`

ANSWER:

(b) 0.64

(c) Triangle shape

(d) 0.64