- #1
KEØM
- 68
- 0
Homework Statement
Sarah and Thomas each roll a die. Whoever gets the higher number wins; if they both roll they same number, neither wins.
a. What is the probability that Thomas wins?
b. If Sarah, rolls a 3 what is the probability that she wins?
c. If Sarah rolls a 3 what is the probability that Thomas wins?
d. If Sarah wins what is the probability that Thomas rolled a 3?
e. If Sarah wins what is the probability that Sarah rolled a three?
Homework Equations
P(A|B) = P(A[tex]\cap[/tex]B)/P(B)
Bayes' Rule
The Attempt at a Solution
For a, is it as simple as they both at the beginning of the game have an equally likely chance of winning so 1/2?
b) If she rolls a 3 then in order for her to win Thomas must roll a 1 or 2 so the probability that she wins is 1/3
c) If she rolls a three then in order for Thomas to win he must roll a 4,5 or 6 so the probability that he wins is 1/2.
d) If Sarah wins she must have rolled a 2,3,4,5, or 6. For Thomas to lose he must have rolled a 1,2,3,4 or 5. So the probability that he rolls a 3 is 1/5.
e) If Sarah wins she must have rolled a 2,3,4,5, or 6. So the probability that she rolls a three is also 1/5.
Is this correct reasoning? Also how do I actually use the relevant equations in this problem?