A standard deck of 52 playing cards is composed of 4 suits. Each mix contains 13 cards. Jacks, Queens, and Kings are considered face cards. Assume three cards are selected without replacement. Calculate the probability of drawing two hearts, followed by a spade.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
13/52 * 12/51 * 13/50 = ?
To calculate the probability of drawing two hearts followed by a spade, we first need to determine the total number of possible outcomes.
In a standard deck of 52 playing cards, there are 13 hearts, 13 spades, and a total of 52 cards.
First, let's calculate the probability of drawing two hearts.
For the first card, there are 13 hearts out of a total of 52 cards, so the probability of drawing a heart on the first draw is 13/52.
For the second card, after one heart has already been drawn (without replacement), there are 12 hearts left out of a total of 51 cards, so the probability of drawing another heart is 12/51.
Now, let's calculate the probability of drawing a spade on the third card.
After drawing two hearts (without replacement), there are still 11 spades left out of a remaining deck of 50 cards, so the probability of drawing a spade is 11/50.
To calculate the probability of these events occurring in sequence, we multiply the individual probabilities together:
(13/52) * (12/51) * (11/50) = 0.052
Therefore, the probability of drawing two hearts followed by a spade is 0.052 or 5.2%.