I've been trying to solve this question, any help would be much appreciated!
There are three coins. 2 coins are fair, the other has two tails. A
random coin from this pile is chosen and tossed, it lands heads. This
is done two more times without replacement.What is the conditional probability that the third toss will land
heads?If X is a random variable which counts the number of heads
total over the three tosses (assuming each coin is tossed exactly
once) what is the expected value E(X)?what is the variance of X?
I believe each coin is tossed only once.
Best Answer
The two-tailed coin can't be the one that was chosen. So one of the two fair coins was chosen, and we know it landed heads. The fair coin that was not chosen could land either heads or tails, with equal probabilities. So the possible values of $X$ are $1$ and $2$, each with probability $1/2$.
As for the conditional probability of the "third toss", the question is a bit ambiguous. Is the coin that was chosen the first toss, or could the coins have been tossed in any order?