Question

a betting game allows the player to first roll a balanced 4-sided die, with faces numbered 1, 2, 3, and 4. After the die is rolled the player randomly draws cards from a standard 52-card deck, selecting the same number of cards as their die roll. For example, if a 3 was rolled than the player selects 3 cards at random from the deck(without replacement). The player wins $5 for every Heart drawn. What is the probability that a player will not win any money when they play this game once?

Answer 1

P(1 & no heart) + P(2 & no heart) + P(3 & no heart) + P(4 & no heart)

1/4 x 39/52 + 1/4 x 39/52 x 39/51 + 1/4 x 39/52 x 39/51 x 39/50 + 1/4 x 39/52 x 39/51 x 39/50 x 39/49