Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the following probabilities of the second card.
P(spade | spade) = 1
P(king | three) = 2
0
To calculate probabilities in this scenario, we need to use the concept of conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred.
1. P(spade | spade):
This probability represents the chance of drawing a spade card as the second card, given that the first card drawn was a spade. Since one spade card has already been removed, we know that there are 12 spade cards remaining in the deck.
The probability of drawing a spade as the second card, given that the first card was a spade, is:
P(spade | spade) = (number of remaining spades) / (number of remaining cards)
There are 12 remaining spades and a total of 51 remaining cards after one is removed. Therefore,
P(spade | spade) = 12 / 51 = 0.235 (approximately)
So, the probability of drawing a spade as the second card, given that the first card was a spade, is approximately 0.235 or 23.5%.
2. P(king | three):
This probability represents the chance of drawing a king as the second card, given that the first card drawn was a three. Since the first card was a three, we know that there are no king cards remaining since a standard deck of cards contains only four kings.
Therefore, P(king | three) = 0, which means the probability of drawing a king as the second card, given that the first card was a three, is 0 or 0%.
It is important to note that when calculating probabilities, we also need to consider the assumption that the cards are drawn randomly and without replacement.