Two cards are drawn without replacement from an ordinary
deck of 52 playing cards. What is the probability that
both are spades if the first card drawn was a spade?
12 Spades left,
so prob = 12/51
Thanks
one is a spade and one is a heart
To calculate the probability that both cards drawn are spades given that the first card is a spade, we need to consider the remaining 51 cards in the deck after the first card is drawn.
The total number of spades in a deck is 13, since there are 13 spades in a standard deck. The probability of drawing a spade as the first card is 13/52, or 1/4.
After the first spade is drawn, there are 12 spades left in the deck, out of the remaining 51 cards. Therefore, the probability of drawing a second spade is 12/51.
To find the probability of both events happening, we multiply the probabilities together:
P(both spades) = P(first spade) * P(second spade | first spade)
P(both spades) = (1/4) * (12/51)
Simplifying this expression gives us:
P(both spades) = 3/52
So, the probability that both cards drawn are spades, given that the first card is a spade, is 3/52.