Question

A Discipline committee is selected by placing the names of 12 teachers in a bag and then randomly drawing 3 of the names. If there are 7 Math teachers and 5 English teachers, what is the probability (as a decimal rounded to the nearest thousandth) that the committee will be made up of all English teachers?

a).159
b).092
c).416
d).045

Answer 1

The probability that a committee of 3 randomly drawn from a pool of 12 teachers with only 5 being English teachers will be made up entirely of English teachers is approximately 0.045.

Step-by-step explanation:

To find the probability that the committee will be made up of all English teachers, we can use the principles of combinatorics and calculate a hypergeometric probability. Since there are 5 English teachers out of a total of 12 teachers, the number of ways to choose 3 English teachers from the 5 available is calculated using the combination formula C(n, k) = n! / (k! * (n-k)!), which gives C(5, 3). Similarly, the total number of ways to choose any 3 teachers from the 12 is C(12, 3). The probability is the ratio of these two numbers.

Calculating C(5, 3) we get:

5! / (3! * (5-3)!) = (5*4*3*2*1) / ((3*2*1) * (2*1)) = 10

Calculating C(12, 3) we get:

12! / (3! * (12-3)!) = (12*11*10*9*8*7*6*5*4*3*2*1) / ((3*2*1) * (9*8*7*6*5*4*3*2*1)) = 220

Thus, the probability is:

P(all English teachers) = C(5, 3) / C(12, 3) = 10 / 220 = 1/22 ≈ 0.045 when rounded to the nearest thousandth.

This is answer choice d.