Two cards are dealt from a standard 52-card deck, one by one, without replacement.
Determine the probability that 2 kings are selected. Show work.
The probability of selecting the first king is 4/52. Once the first king is selected and removed from the deck, there are 3 kings left in a deck of 51 cards. Therefore, the probability of selecting a second king after the first king is 3/51. To find the probability of both events occurring, we multiply the probabilities:
(4/52) x (3/51) = 1/221
Therefore, the probability of selecting 2 kings from a standard 52-card deck, one by one, without replacement is 1/221.
To determine the probability of selecting 2 kings from a standard 52-card deck without replacement, we need to calculate the probability of each card being selected.
Step 1: Determine the probability of selecting the first king.
There are 4 kings in a standard deck, so the probability of selecting the first king is 4/52 (4 kings out of 52 cards).
Step 2: Determine the probability of selecting the second king.
After the first card is selected, there are now 51 cards remaining in the deck. However, since one king has already been selected, there are only 3 kings left. So, the probability of selecting the second king is 3/51 (3 kings out of 51 cards).
Step 3: Multiply the probabilities.
Since the two cards are selected one by one, without replacement, we multiply the individual probabilities to find the probability of both events happening.
Probability of selecting 2 kings = (4/52) * (3/51) = 12/2652 ≈ 0.0045
Therefore, the probability of selecting 2 kings from a standard 52-card deck, one by one, without replacement is approximately 0.0045.