Question

Summer Campers John and Ryan Are Trying To Earn Thier Archery Merit badges Each Boy has 30 Arrows and Must hit the center of the Target More Than 10 Times John hits the Center 1 Time for every 3 Arrows he Shoots. Ryan Hits the Center 2 times for every 5 arrows he shoots.which boy earns an Archery Mertit Badge

Answer 1

Ryan

Explanation:

Let's calculate the probabilities of John and Ryan hitting the target center

Let P(J) and P(R) be the respective probability representations

For John

John hits the center 1 time for every 3 tries(arrows)
Therefore

`P(J) = (1)/(3)`

Out of 30 arrows (and therefore 30 attempts) the expected number of times that John can hit the center is given by

`30\cdot (1)/(3) = 10\\`

Since you need to hit the center more than 10 times, John is not expected to win the merit badge

For Ryan

Ryan Hits the center 2 times for every 5 arrows (attempts)

`P(R) = (2)/(5)`

With 30 arrows the expected number of times that Ryan hits the target is:

`30\cdot (2)/(5) = 18\\\\`

So Ryan is expected to win the Archery Merit Badge.

Important Note

Here you have to be careful of the words you use and interpret the results with some reality checks.

Probabilities after all are based on previous trials and represent only an estimate of guarantees of future events. That's why I have repeatedly used the word expected.

After all, John maybe able to hit the center a 11th time and thus he too will earn a merit badge.

In my opinion a poorly worded question