A restaurant is open 7 days a week. 3 employees get to select 1 day off next
week randomly. What is the probability that all three select the same day,
given that all three select a day beginning with the same letter?
Suppose the 3 employes are Tom, Dick, and Harry.
There are only 4 successful ways, all choose Tues., Thurs., Sat., or Sun.
So the numerator of the desired probability is 4.
Now we find the number of possible ways that could be the given case:
We can choose the letter for the days to begin with, T or S. 2 ways.
We can choose the day for Tom 2 ways.
We can choose the day for Dick 2 ways.
We can choose the day for Harry 2 ways.
That's 2*2*2*2 = 16 ways. That's the denominator.
Answer: 4/16 = 1/4.
Edwin