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We flip a fair coin (independently) three times. Define the following events:

A = "the number of tails is odd"

B = "the number of heads is even"

What is the probability of event A and event B?

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HINT: $A=\{HHT,HTH,THH,TTT\}$ and $B=\{HHT,HTH,THH,TTT\}$

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    $\begingroup$ Wouldn't 0 heads be valid for B? $\endgroup$ – RandomUser Apr 25 '14 at 21:34
  • $\begingroup$ So Pr(A)= 4/2^3 ? since total possible outcomes are 2^3? $\endgroup$ – Andrew Apr 25 '14 at 21:34
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    $\begingroup$ @RandomUser I was just about to suggest this. $\endgroup$ – homegrown Apr 25 '14 at 21:35
  • $\begingroup$ @RandomUser: Yes you are right. Mistake! $\endgroup$ – Argha Apr 25 '14 at 21:35
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    $\begingroup$ @jnh Yup, it says I cant accept for 1 more minute. Will do so. $\endgroup$ – Andrew Apr 25 '14 at 21:44
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The probability of an odd number of heads is the same as the probability of an odd number of tails - Prob(H)=Prob(T). And either the number of heads or tails are odd - 2 Prob(T) = 100%.

So 50%.

The same for an even number.

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Whichever event you're betting on, A or B, it all comes down to the last flip: if it comes up one way you win, the other way you lose. Assuming it's a fair coin, your probability of winning is 50%.

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