Suppose two cards are drawn from a well-shuffled deck of 52-cards. What is the probability that both cards are face cards?
What formula would I use?
how many face cards are there?
chance of getting 1: ?
with one missing, chance of getting another: ?
multiply the two.
To find the probability of drawing two face cards from a deck of 52 cards, we can use the concept of combinations.
First, we need to determine the total number of ways two cards can be drawn from the deck, which is given by the combination formula: nCr = n! / (r!(n - r)!), where n is the total number of items and r is the number of items we want to choose.
In this case, since we are drawing 2 cards from a deck of 52 cards, the total number of ways of drawing two cards is equal to C(52, 2).
Next, we need to determine the number of ways we can draw two face cards. In a deck of 52 cards, there are 12 face cards (4 kings, 4 queens, and 4 jacks). Therefore, the number of ways of drawing two face cards is equal to C(12, 2).
Finally, to calculate the probability, we divide the number of favorable outcomes (drawing two face cards) by the total number of possible outcomes (drawing any two cards) using the formula:
Probability of drawing two face cards = (number of ways of drawing two face cards) / (number of ways of drawing two cards)
So, the formula you would use is:
P(drawing two face cards) = C(12, 2) / C(52, 2)