We are told that there are 40 students, 9 camp counselors, and 5 teachers at Camp Kern. There are three activities that a person can do: hiking, horseback riding, and a canoe trip. Each person is assigned to only one of these activities. Let's make a to organize the given information.
|
Hiking
|
Horseback Riding
|
Canoe Trip
|
Total
|
Student
|
9
|
17
|
|
40
|
Camp Counselor
|
2
|
|
3
|
9
|
Teacher
|
|
2
|
2
|
5
|
Since we know the total number of students, camp counselors, and teachers, we can calculate the missing data.
|
Hiking
|
Horseback Riding
|
Canoe Trip
|
Total
|
Student
|
9
|
17
|
14
|
40
|
Camp Counselor
|
2
|
4
|
3
|
9
|
Teacher
|
1
|
2
|
2
|
5
|
We will find the of a randomly selected person being a student on the canoe trip
A or a camp counselor horseback riding
B. The
A and
B are . Therefore, the probability of selecting a student on the canoe trip
A or a camp counselor on a horse
B is the sum of their individual probabilities.
P(A or B)=P(A)+P(B)
Let's first calculate the probability of
A. This probability can be found by the of the number of students on the canoe trip to the total number of people at the camp.
P(A)=total number of peoplestudents on the canoe trip
Looking at the table, we will substitute the values into this ratio and calculate it.
P(A)=Total number of peopleStudents on the canoe trip
P(A)=40+9+514
P(A)=5414
Let's now calculate the probability of a randomly selected person being a camp counselor riding a horse
B by the same method used to find
P(A).
P(B)=Total number of peopleCamp counselors on a horse
Using the table, we will substitute the values into the ratio and calculate
P(B).
P(B)=Total number of peopleCamp counselors on a horse
P(B)=40+9+54
P(B)=544
Finally, we will substitute the ratios
P(A)=5414 and
P(B)=544 into the and solve it for
P(A or B).
P(A or B)=P(A)+P(B)
P(A or B)=5414+544
P(A or B)=5418
P(A or B)=31
The probability that a randomly selected person will be a student on a canoe trip
or a camp counselor riding a horse is
31.