Question

Three cards are drawn with replacement from a standard deck. What is the probability that the first card will be a heart, the second card will be a black card, and the third card will be a face card? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Answer:

The probability that the first card is a heart, the second one is a black card and the third card is a face card is 3/104.

Step-by-step explanation:

Since there is replacement, and each draw is independent of each other, then we can compute the probability of each draw separately and then multiply them toguether to obtain the probability of the full event.

There is 52 cards in a standard deck (with no jokers). There are 13 hearts in total, so the probability that a heart is drew is 13/52 = 1/4.

There are 2 suits that involves black cards, spades and clubs, thus, there are 13*2 = 26 black cards out of a total of 52, exactly half. THus, the probability that the second card is a black card is 1/2.

Each suit has 3 face cards, therefore there are a total of 12 face cards out of 52 total, as a consecuence, the probability that you draw a face card as your third card is 12/52 = 3/13.

Using this probabilities, we can conclude that the probability of drawing a heart followed by a black card and then followed by a face card is 1/4*1/2*3/13 = 3/104.