Question

A warehouse employs 22 workers on first shift and 14 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment. Find the Probability of choosing:
a. All first-shift workers
b. All second-shift workers
c. Six first-shift workers
d. Four second-shift workers

Answer 1

36 all together.
22 first
14 second
8 random chosen

A) all first shift:
One is pulled 22/36
Second is pulled 21/35
Third is pulled 20/34
Fourth 19/33
Fifth 18/32
Sixth 17/31
Seventh 16/30
Eighth 15/29

Multiply all those together
Probability of all first shift is 0.010567296996663
(That means it's not happening anytime soon lol)

B) one worker 14/36
Second 13/35
Third 12/34
Fourth 11/33
Fifth 10/32
Sixth 9/31
Seventh 8/30
Eighth 7/29

Multiply all those together
Probability of all second shift is 0.000099238805645
(That means it's likely to see 100x more picks of all first shift workers before you see this once.. lol)

C) 22/36
21/35
20/34
19/33
18/32
17/31

Multiply..
Probability.. 0.038306451612903


D) 14/36
13/35
12/34
11/33

X... p=0.016993464052288


Probably not correct, haven't done probability in years.