Probability : Sampling Without Replacement - Card Hands

6. A hand of 4 cards contains one card of each suit ( I,e., one Heart, one Diamond, One Club and one spade). Simon uses this hand to play a game for which the rules are as follows: (1) When a Heart is drawn, the game stops immediately. (2) If the Diamond is drawn, the Diamond is set aside and not replaced (so that when the game continues there are only 3 cards in the hand). (3) If a black card is drawn, that black card is set aside and another Heart is put into the hand in its place (so the game continues with the same number of cards as before). Simon draws cards from the hand, one at a time, following these rules, until he draws a Heart (which may, of course, happen on the first draw, or on any subsequent draw). If it is known that Simon drew at least 3 cards while playing the game, what is the probability that the Diamond was still in the hand when the game stopped? Hint: Draw a probability tree.

Solution Summary

Sampling Without Replacement for Card Hands is investigated. The solution is detailed and well presented.