Two cards are randomly drawn from a standard deck without replacing the card after the first draw. Find the probability of drawing a spade followed by a heart. Please type your answer as a fraction. Do not forget to reduce if needed!
prob a spade = 13/52
now a heart = 13/51
so prob(your event) = (13/52)(13/51) = 13/204
To find the probability of drawing a spade followed by a heart, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. We are drawing two cards from a standard deck without replacing the first card, which means there are 52 cards in the deck initially, then 51 cards for the second draw.
To calculate the number of favorable outcomes, the first card should be a spade (there are 13 spades in the deck), and the second card should be a heart (there are 13 hearts in the deck).
So, the number of favorable outcomes is 13 * 13 = 169.
Therefore, the probability of drawing a spade followed by a heart is:
Probability = (Number of Favorable Outcomes) / (Number of Possible Outcomes)
Probability = 169 / (52 * 51)
Now, let's simplify this fraction. Start by canceling out any common factors between the numerator and the denominator:
169 = 13 * 13
52 = 13 * 4
51 = 17 * 3
So, the fraction becomes:
Probability = (13 * 13) / (13 * 4 * 17 * 3)
We can further simplify this fraction by canceling common factors:
Probability = (13 * 1) / (4 * 17 * 3)
Probability = 13 / (4 * 17 * 3)
Finally, multiply the remaining numbers in the denominator:
Probability = 13 / 204
Therefore, the probability of drawing a spade followed by a heart is 13/204.