I have three 3 types of computers, 57% are PC's, 29% are Mac's and 14% are Unix. I need to find the probability that the next 3 calls with result in:
all are Macs
none are PCs
at least 1 is a Unix.
You haven’t shown any work to indicate what you know or have tried (and your problem statement is not entirely clear), but I’ll give you the first one (if I understand what you are asking):
(.29)(.29)(.29) = .024389 or about 2.4%
and the second one:
(1 - .57)(1 - .57)(1 - .57) = .079507 or about 8%
Can you see how this works?
The third problem will be a combination of events. “At least 1” means 1 or 2 Unix in this case. You could figure out all the possible combinations that have either 1 or 2 Unix, calculate the probability for each, and then add them up.
Alternatively, you could find the probability that there are 0 Unix and subtract that answer from 1. (That would be the easier approach.)
No Unix combos:
PPP
MMM
PPM
PMP
MPP
MMP
MPM
PMM
Just calculate the probability for each combo listed above, add them together, and subtract the answer from 1.
Note: You could also draw a probability tree diagram for this problem and calculate the probability along each of the 27 branches (or along just the branches you want to know about).
