# Independence

• Oct 9th 2008, 10:44 AM
slevvio
Independence
A (possibly biased) coin is tossed twice. The result 'heads' is noted if the coin lands heads up on the first toss and tails up on the second toss (HT). In a similar way, the result 'tails' is noted if the outcome is TH. HH and TT are ignored, the entire experiment being repeated until either HT or TH occurs. Show that the result 'heads' is noted with probability 0.5 (however biased the coin).

Thanks in advance any help with this would be appreciated.
• Oct 9th 2008, 06:20 PM
mr fantastic
Quote:

Originally Posted by slevvio
A (possibly biased) coin is tossed twice. The result 'heads' is noted if the coin lands heads up on the first toss and tails up on the second toss (HT). In a similar way, the result 'tails' is noted if the outcome is TH. HH and TT are ignored, the entire experiment being repeated until either HT or TH occurs. Show that the result 'heads' is noted with probability 0.5 (however biased the coin).

Thanks in advance any help with this would be appreciated.

Let p be the probability that a coin comes up heads on a single toss. Then 1 - p is the probability that a coin comes up tails on a single toss.

Pr(Heads) = Pr(HT) = p(1 - p).

Pr(Tails) = Pr(TH) = (1 - p)p.