If three cards are drawn at random from a standard deck of 52 playing cards, what is the probability that at least one of the cards is a face card: that is, one of the cards is a kind, queen, or jack?
P(1) = 12/52
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(2) = 12/52 * 11/51
p(3) = 12/52 * 11/51 * 10/50
P(4) = 12/52 * 11/51 * 10/50 * 9/49
The question is asking for the probability of 1, 2, 3 or 4 face cards.
Either-or probabilities are found by adding the individual probabilities.
To find the probability that at least one of the three cards drawn is a face card, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When three cards are drawn from a standard deck of 52 playing cards, there are a total of 52C3 possible outcomes. This can be calculated using the combination formula: nCk = n! / (k!(n-k)!), where n represents the total number of items and k represents the number of items chosen.
Favorable outcomes:
To determine the number of favorable outcomes, we need to consider two cases:
1. Drawing exactly one face card: There are 3 face cards in each suit (king, queen, and jack), and 4 suits in a deck. Hence, there are 3 * 4 = 12 ways to choose exactly one face card. We also need to choose two non-face cards from the remaining 48 cards, which can be done in 48C2 ways.
2. Drawing two or three face cards: There are three possibilities:
a. Drawing exactly two face cards: This can be done in 12C2 ways.
b. Drawing exactly three face cards: This can be done in 12C3 ways.
To obtain the number of favorable outcomes, we sum up the outcomes from each case:
Number of favorable outcomes = 12 * 48C2 + 12C2 + 12C3
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Plugging the values into the formula, we can find the answer.