A coin is biased in such a way that on each toss the probability of heads is and the probability of tails is . The outcomes of the tosses are independent. A player has the choice of playing Game A or Game B. In Game A she tosses the coin four times and wins if exactly three outcomes are heads. In Game B she tosses the coin five times and wins if the first three outcomes are the same and the last two outcomes are the same. How do the chances of winning Game A compare to the chances of winning Game B?
The probability of winning Game A is less than the probability of winning Game B.
The probability of winning Game A is less than the probability of winning Game B.
The probabilities are the same.
The probability of winning Game A is greater than the probability of winning Game B.
The probability of winning Game A is greater than the probability of winning Game B.