In fact, all six sequences that have exactly two hearts have the same probability.ġ) Because we draw with replacement, every draw is independent from each-other.Ģ) Note that each draw event is a Bernoulli trial because it only has two possible outcomes. We see that only six sequences have exactly two hearts: HHTT, HTHT, HTTH, THHT, THTH, TTHH. The 16 possible sequences (let H represent a heart and T represent not a heart): We can figure out the probability of each sequence that has exactly two hearts, then add them up.
Thus, there are 2 4 = 16 unique sequences we could draw. We draw a sequence of four cards, and each card has two possible results: a heart or not a heart. There are a couple ways to look at this problem. The 52 deck of cards has 13 hearts, so the probability of drawing a heart would be 0.25, and the probability of not drawing a heart would be 0.75.
