Question

A committee of three people is selected at random from a set containing of seven teachers, six parents of students, and four alumni. • What is the probability the committee consists of all teachers? • What is the probability of the even that the committee consists of no teachers?

Answer 1

Step 1

State the expression for the probability of an event

`\text{Probability of an event = }\frac{Number\text{ of required events}}{\text{Total number of events}}`

Total number of events = 7+6+4 = 17

Step 2

Find the probability for selection of 3 teachers

`\text{The probability to select a teacher at the first selection = }(7)/(17)`
`\text{The probability to select a teacher at the second selection=}(6)/(16)=(3)/(8)`
`\text{The probability to select a teacher at the third selection = }(5)/(15)=(1)/(3)`

Therefore

`The\text{ probability the committ}ee\text{ consists of all teachers = }(7)/(17)*(3)/(8)*(1)/(3)=(7)/(136)`

Step 3

Find the probability the committee consists of no teachers

Total number of non-teachers in the population = 6 + 4=10

Therefore,

`\text{The probability the committee consists of no teachers on the 1st selection = }(10)/(17)`
`\text{The probability the committee consists of no teachers on the 2nd selection= }(9)/(16)\text{ }`
`\text{The probability the committee consists of no teachers on the 3rd selection }=\frac{8}{15^{}}`

Therefore,

`\text{The probability the committe consists of no teacher = }(10)/(17)*(9)/(16)*(8)/(15)=(3)/(17)`