A standard deck of cards has four different suits:hearts ,diamonds ,spades, and clubs.Each suit has 13 cards, making a total of 52.Two cards are drawn without replacement. What is the probability of drawing first a heart, and then a spade?
Assuming the first card is not replaced
prob(heart, then spade)
= (13/52)(13/51)
= 13/204
13/52
To find the probability of drawing first a heart and then a spade, we need to calculate the probability of each event happening separately and then multiply them together.
Step 1: Probability of drawing a heart (without replacement)
In a standard deck of 52 cards, there are 13 hearts. After drawing one card, there are 51 cards left, and 12 hearts remaining. Therefore, the probability of drawing a heart first is 13/52.
Step 2: Probability of drawing a spade (without replacement)
After drawing a heart as the first card, there are 51 cards remaining in the deck. Out of those, there are 13 spades. Therefore, the probability of drawing a spade second is 13/51.
Step 3: Multiply the probabilities
To find the probability of both events happening, we multiply the probabilities together:
(13/52) * (13/51) = 169/2652
Simplifying this fraction, we get:
169/2652 = 13/204
So, the probability of drawing first a heart and then a spade is 13/204.