- #1
philipSun
- 9
- 0
Hello everybody. I have a problem, which is following.
AA tosses a coin 3 times and BB 2 times. AA will win, if he gets more heads than BB.
What is the probability that AA wins? Total probability is probably needed in this.
My solution:
first, this formula,
P(b) = P(a) P(b | a ) + P(a^c) P(b | a^c)
and events are;
a = happens, that there will be heads
b = happens, that there will be tails
a^c = a won't happen
In best case for AA;
a = 1-3 * a
b = 0-2 * a
a wins
In best case for BB;
b = 1-2 * a
a = 0-1 * a
now, a won't win.
P(b) = P(a) P(b | a ) + P(a^c) P(b | a^c)
P(2) = P(3) P(2 | 3 ) + P(0) P(2 | 0)
P(2) = P(3) P(2 | 3 ) + P(0) P(2 | 0)
This is as fas as I can go.
AA tosses a coin 3 times and BB 2 times. AA will win, if he gets more heads than BB.
What is the probability that AA wins? Total probability is probably needed in this.
My solution:
first, this formula,
P(b) = P(a) P(b | a ) + P(a^c) P(b | a^c)
and events are;
a = happens, that there will be heads
b = happens, that there will be tails
a^c = a won't happen
In best case for AA;
a = 1-3 * a
b = 0-2 * a
a wins
In best case for BB;
b = 1-2 * a
a = 0-1 * a
now, a won't win.
P(b) = P(a) P(b | a ) + P(a^c) P(b | a^c)
P(2) = P(3) P(2 | 3 ) + P(0) P(2 | 0)
P(2) = P(3) P(2 | 3 ) + P(0) P(2 | 0)
This is as fas as I can go.