Final answer:
The probability of drawing a diamond from a 52-card deck is 1/4. The probability of drawing a King followed by a 2 without replacement is 4/663. These probabilities are calculated by considering the number of desired outcomes divided by the total number of possible outcomes for each event, considering that the second event is dependent on the first.
Step-by-step explanation:
To find the probability of drawing a specific card or combination of cards from a standard 52-card deck, we use basic probability principles. In a 52-card deck, there are 4 suits, and diamonds are one of those suits. Each suit has an equal number of cards, which is 13.
Probability of a Diamond
To calculate the probability of drawing a diamond from a standard deck of 52 cards, we need to divide the number of diamond cards by the total number of cards in the deck.
Total number of cards = 52
Number of diamonds = 13
Probability of drawing a diamond = Number of diamonds / Total number of cards = 13/52 = 1/4
Probability of Drawing a King Followed by a 2
For the probability of drawing a king followed by drawing a 2, calculations change because the draw is without replacement. When the first card is drawn, there is one less card in the deck, so the total number of possible outcomes for the second draw is 51.
Probability of drawing a King first = Number of kings / Total number of cards = 4/52
After drawing a King, the probability of drawing a 2 = Number of 2s(remaining) / Remaining cards in the deck = 4/51
Total probability = Probability of first King * Probability of second 2 = (4/52) * (4/51) = 1/13 * 4/51 = 4/663
Note that the total probability is found by multiplying the probabilities of each sequential event because we are considering a compound event where both events must happen.