Answer:
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event/total outcome of event
Given 5 individuals with 4, 6, 7, 10, and 15 years of teaching experience.
Since two of these 5 individuals are randomly selected to serve on a personnel review committee, total possible outcome = 5C2 (randomly selecting 2 personnel out of 5 )
5C2 = [tex]\frac{5!}{(5-2)!2!}[/tex]
[tex]= \frac{5!}{3!2!}\\ = \frac{5*4*3!}{3!*2} \\= 10\ possible\ selections\ can\ be\ done[/tex]
To get the probability that the chosen representatives have a total of at least 16 years of teaching experience, first we need to find the two values that will give a sum of years greater that or equal to 16 years. The possible combination are as shown;
4+15 = 19years (first reps)
6+10 = 16years (second reps)
6+15 = 21years (third reps)
7+10 = 17 years (fourth reps)
7+15 = 22 years (fifth reps)
10+15 = 25 years (sixth reps)
This shows that there are 6 possible ways to choose the representatives that have a total of at least 16 years of teaching experience
Total outcome = 10
expected outcome = 6
Probability that the chosen representatives have a total of at least 16 years of teaching experience = [tex]\frac{6}{10} = \frac{3}{5}[/tex]
