STA 4821 Exam (in class, open book) 30 Points 70 Minutes Fall 08
I pledge my honor that I have neither given nor received aid on this exam.
_________________________________________ ________________
NAME SSN (last 4 digits)
Show all work (attach work pages). Write on one side of page only.
Write answers in space provided. Staple in upper left-hand corner.
Consider three identical-looking dice. Two of the dice are ordinary fair dice (six equally-likely faces,
numbered 1,2,...,6), but the third die is "loaded" (the face that ordinarily has a 1 has a 6 instead; that is, the
loaded die has two 6's, on opposite faces). Fran and Ron each choose a die at random, and the remaining
die is discarded.
Suppose that Fran and Ron roll their dice simultaneously.
1. Find the probability that Fran rolls a 6. 1) ______________
2. Find the probability that Ron rolls a 6. 2) ______________
3. Find the probability that Fran rolls a 6 and Ron 3) ______________
rolls a 6.
4. Find the probability that Fran rolls a 6 if it is 4) ______________
known that Ron rolled a 6.
Now suppose that Fran rolls her die again (that is, she rolls the same die twice).
5. Find the probability that Fran's second roll is a 6. 5) ______________
6. Find the probability that Fran's first roll is a 6 and her 6) ______________
second roll also is a 6.
