Question

jimmy is playing a game at a state fair, where he is throwing a dart at a target. for each throw, jimmy can choose to throw the dart at a rectangular target or at a circular target. to score a point during the game, jimmy must hit the bulls - eye of the target that he chooses. so far, jimmy has thrown the dart at the rectangular target 6 times, and he has thrown the dart at the circular target 12 times.
when jimmy has thrown the dart at the rectangular target, he has missed the bulls - eye 3 times. when jimmy has thrown the dart at the circular target, he has missed the bulls - eye 10 times.
based on the information above, if jimmys goal is to score a point on his next throw, which target should he choose?
a. rectangular
b. circular
c. there is not enough information to determine the target that jimmy should choose.
d. neither target has an advantage.

Explanation:

Step1: Calculate the success rate for the rectangular target

The number of attempts at the rectangular target is \(n_{r}=6\), and the number of misses is \(m_{r} = 3\). So the number of hits \(h_{r}=6 - 3=3\). The success rate \(P_{r}=\frac{h_{r}}{n_{r}}=\frac{3}{6}=\frac{1}{2}\)

Step2: Calculate the success rate for the circular target

The number of attempts at the circular target is \(n_{c}=12\), and the number of misses is \(m_{c}=10\). So the number of hits \(h_{c}=12 - 10 = 2\). The success rate \(P_{c}=\frac{h_{c}}{n_{c}}=\frac{2}{12}=\frac{1}{6}\)

Step3: Compare the success rates

Since \(\frac{1}{2}>\frac{1}{6}\) (because \(\frac{1}{2}=\frac{3}{6}\) and \(\frac{3}{6}>\frac{1}{6}\))

Answer:

A. rectangular