Question

A manufacturing facility has 21 high pressure valves manufactured by Company A and 14 valves manufactured by Company B. Only six valves can be installed in any given day If the 6 valves are chosen at random, what is the probability that 5 or fewer are from Company A?

Answer 1

0.9666

Explanation:

Given that a manufacturing facility has 21 high pressure valves manufactured by Company A and 14 valves manufactured by Company B.

6 valves are chosen at random

Total no of ways of randomly choosing 6 valves = (21+14)C6

=
`35C6 = (35*34*33*32*31*30)/(6!) \\=1623160`

Choosing 5 or fewer form company A can be as follows

(A,B) = (0,6) (1,5) (2,4)(3,1)(4,2) (5,1)

This can be written as 1-Prob of choosing all 6 from A

No of ways of choosing all 6 from A = 21C6 = 54264

Hence the probability that 5 or fewer are from Company A

=
`1-(54264)/(1623160) \\=1-0.0334\\=0.9666`