Respuesta :
Step 1
State the expression for the probability of an event
[tex]\text{Probability of an event = }\frac{Number\text{ of required events}}{\text{Total number of events}}[/tex]Total number of events = 7+6+4 = 17
Step 2
Find the probability for selection of 3 teachers
[tex]\text{The probability to select a teacher at the first selection = }\frac{7}{17}[/tex][tex]\text{The probability to select a teacher at the second selection=}\frac{6}{16}=\frac{3}{8}[/tex][tex]\text{The probability to select a teacher at the third selection = }\frac{5}{15}=\frac{1}{3}[/tex]Therefore
[tex]The\text{ probability the committ}ee\text{ consists of all teachers = }\frac{7}{17}\times\frac{3}{8}\times\frac{1}{3}=\frac{7}{136}[/tex]Step 3
Find the probability the committee consists of no teachers
Total number of non-teachers in the population = 6 + 4=10
Therefore,
[tex]\text{The probability the committee consists of no teachers on the 1st selection = }\frac{10}{17}[/tex][tex]\text{The probability the committee consists of no teachers on the 2nd selection= }\frac{9}{16}\text{ }[/tex][tex]\text{The probability the committee consists of no teachers on the 3rd selection }=\frac{8}{15^{}}[/tex]Therefore,
[tex]\text{The probability the committe consists of no teacher = }\frac{10}{17}\times\frac{9}{16}\times\frac{8}{15}=\frac{3}{17}[/tex]