Exercise 1 Page 819

If two events cannot occur simultaneously, then they are said to be mutually exclusive.

Practice makes perfect

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 two-way table 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 probability of a randomly selected person being a student on the canoe trip A or a camp counselor horseback riding B. The events A and B are mutually exclusive. 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 ratio of the number of students on the canoe trip to the total number of people at the camp. P(A)=students on the canoe trip/total number of people Looking at the table, we will substitute the values into this ratio and calculate it.

P(A)=Students on the canoe trip/Total number of people

SubstituteValues

Substitute values

P(A)=14/40+9+5

AddTerms

Add terms

P(A)=14/54

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)=Camp counselors on a horse/Total number of people Using the table, we will substitute the values into the ratio and calculate P(B).

P(B)=Camp counselors on a horse/Total number of people

SubstituteValues

Substitute values

P(B)=4/40+9+5

AddTerms

Add terms

P(B)=4/54

Finally, we will substitute the ratios P(A)= 1454 and P(B)= 454 into the equation and solve it for P(AorB).

P(AorB)=P(A)+P(B)

SubstituteII

P(A)= 14/54, P(B)= 4/54

P(AorB)= 14/54+ 4/54