Coin toss - part 2
If you have not seen part 1 yet, check it here .
I have two coins, one of them is fair and has a 50% probability of being either heads or tails, the other is biased having a 90% probability of being heads and a 10% probability of being tails.
You take one of the coins at random and toss it twice. If I tell you that you grabbed the biased coin and on the first toss you get tails, the probability of getting tails in the second toss increases, decreases, or stays the same?
Note: Assume that I don't lie
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The coin can be the biased coin or the fair coin and each of them will give you heads or tails with their respective probability, so we can write the probability of a coin toss coming out as tails by writing:
P ( T ) = P ( C = F ) P ( T ∣ C = F ) + P ( C = B ) P ( T ∣ C = B )
but you already know that you have the biased coin which means that:
P ( T ) = P ( T ∣ C = B ) = 0 . 1
If you solved part 1, you may have realized that without knowing which coin you picked, the first and second toss are not independent random variables, but upon learning that information, they do become independent random variables. This is an example of a conditional independence