a. What is the probability that A and B call the same number?
b. What is the probability that A and B call a specific number?
the probability that A calls a specific number:1/200
the probability that B calls the same specific number: 1/200
1/40000 is the probability of both A and B calling the same, prespecified.
This might be confusing, but try to look at it this way, and assume the numbers are simply 1,2,3,4...200
A could call any of these numbers, so there's a 1/200 chance of A calling a specific number, say, #153
B could call any of these numbers, so there's a 1/200 chance of B calling a specific number, say, #153
1/40000 is the chance of A and B both calling #153.
but, the odds of A and B calling the same number (any number) is still 1/200.
I can try again if this makes no sense.
The easiest way to explain 1 is to say:
No matter what number A calls, there is a 1/200 chance that B will match it. Hence, the prob is 1/200.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993