There are 3 lottery tickets one can choose from:
And the formula for computing the probabilities of final outcomes when a coin is flipped between lotteries yields
So there are 3 different probabilities here. The first one, is the probability of the outcome being dollars, which is (the probability of getting lottery A from the coin flip) x (the probability of the outcome being dollars). That makes sense from the table above. But the second one, , the probability of the outcome being dollars should be or . Why then is it ???
And the formula for computing the probabilities of final outcomes when a coin is flipped between lotteries yields
So there are 3 different probabilities here. The first one, is the probability of the outcome being dollars, which is (the probability of getting lottery A from the coin flip) x (the probability of the outcome being dollars). That makes sense from the table above. But the second one, , the probability of the outcome being dollars should be or . Why then is it ???