Three people go to the market in the morning with the following probabilities: 1/2, 2/3, and 3/4. What is the likelihood that two go to the market on a given morning?
We'll have to work out the probabilities for all three combinations of two, where one stays home . Let's call the people
We'll define the probabilities by the letter
Then we get (remember "and" means multiply)
Since these combinations are mutually exclusive we add :
If the question had been "at least two" we would have to add:
If you had just added the probabilities of