Harry and Mary take turns flipping a biased coin with bias p (0, 1), with Harry

Question

Harry and Mary take turns flipping a biased coin with bias p (0, 1), with Harry flipping the first coin. The first person to flip a heads wins the coin. Find the probability that Harry wins the coin. Recall the setup of the previous problem. For which values of p is it beneficial to be the first person to flip the coin? Recall the setup of the previous problem. Now, Harry flips the coin first, then Mary Slips twice, then Harry flips once, then Mary flips twice, etc. Find the probability that Harry wins the coin. Recall the setup of the previous problem. For which values of p is it beneficial to be the first person to flip the coin?

Explanation / Answer

Harry and Mary tossed a coin

If they tossed a coin one time probability of getting one head or one tail is 1/2

From the geometric expression

P(E)= P(X=1)+P(X=3)+P(X=5)+.........

P(E) = 1/2+1/8+1/32+........

= (1/2) - (1/2)(-3/8)^n

= 1/2+3/16

= 11/16 = 0.68

9. For odd counts first person can win the game

10. For the given series we can write the series as

Tossing a coin doesn't mean that winning the toss

So, winning a game gives probability as above

11. Odd values of P makes first person to win

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