Hello everybody. I have a problem, which is following.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Toss a coin, probability

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