Probability problem - help!

[Zander]

I'm hoping there are some statisticians on the boards who can help with this probability problem:

You have a bunch of a particular denomination of coin from a certain country. It is known that when the coin is tossed, heads (H) comes up more often than tails (T) because the coin is not evenly weighted. Precisely how much more often it comes up H than T is not known.

If you toss two such coins is the probability of HH or TT equal to the probability of HT or TH? In other words, is a same face outcome as likely as a different one? Or to phrase it in yet another way, can a biased coin be used by this method to create a 50/50 chance?

I think the answer is no. If, for example, the probability of tossing H is .80 and, obversely, of tossing T is .20, then HT or TH has a probability of .32 (=.80 x .20 + .20 x .80) but HH or TT has a probability of .68 (=.80 x .80 + .20 x .20). Is that right?

 

[FireLance]

Your calculations look right to me.

In any case, consider the extreme case where P(H) = 1. No way you can get a 50-50 chance on that.

 

[Zander]

Firelance,

Thanks for your reply.

The reason I asked is that I wanted to know if shen bei, sometimes called xiao bei, are fair as they are normally used. Being in Singapore, you might know what I'm talking about.