There are 2000 people.
There are 1050 office workers, so 950 drive cars.
But there are 1150 who drive cars:1150-950=200 are both office workers and drive cars.
There are 1150 car drivers, so 850 are office workers.
But there are 1050 office workers:1050-850=200 are both office workers and drive cars.
But there are 2000 people so 200 people must be office workers and drive cars.
Looking at it three ways says there are 200 people who are office workers and who drive cars.
You have workers(W), drivers(D), and workers who drive(WD).
You choose two people.
The possibilities are W and W, W and D, D and D, W and WD, D and WD, and WD and WD.
To get a worker and a driver, you must get W and D, W and WD, D and WD, or WD and WD.
The probabilities for W and D are (1050/2000)(1150/1999)=(0.525)(0.575)=0.301875
The probabilities for W and WD are (1050/2000)(200/1999)=(0.525)(0.100)=0.052526
The probabilities for D and WD are (1150/2000)(200/1999)=(0.575)(0.100)=0.057528
The probabilities for WD and WD are (0.1)(0.09954)=0.00995
0.301875+0.052526+0.057528+0.00995=0.0.42188=42.188% probability to choose a worker and a driver
Another thought:the probability of getting a D and W
is the same as 1-probability of not getting a D and W
The only way to do this is by getting DD or WW.
These probabilities are 0.525*0.5247=0.27546
Add these to get 0.6059 and 1-0.6059=0.3941=39.41% which differs slightly from 42.188% !
Seeing that I posted three times and they were lost I'll try posting here.
Probability=# of favorable outcomes/total # of equally likely outcomes
The rest of the outcomes come from WW, DD, WD WD, W WD, and D WD.
They are 360,825, 450,775, 19,900, 170,000, and 190,000.
Total of all outcomes=1,999,000