Suppose 5 cards are drawn, without replacement, from a standard bridge deck of 52 cards. Find the probability of drawing 4 clubs and 1 non- club.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
13/52 * 12/51 * 11/50 * 10/49 * (13*3)/48 = ?
To find the probability of drawing 4 clubs and 1 non-club, we first need to determine the total number of ways to draw 5 cards from a standard deck of 52 cards.
The total number of ways to choose 5 cards from 52 can be calculated using the combination formula, denoted as "n choose k" and represented as C(n,k) or nCk. In this case, we want to calculate C(52, 5).
C(52, 5) = 52! / (5! * (52 - 5)!)
Simplifying the expression:
C(52, 5) = 52! / (5! * 47!)
Now, we need to determine the number of ways to draw exactly 4 clubs and 1 non-club.
First, we calculate the number of ways to choose 4 clubs from the 13 clubs in the deck. This can be calculated as C(13, 4).
C(13, 4) = 13! / (4! * (13 - 4)!)
After that, we calculate the number of ways to choose 1 non-club from the remaining 39 cards in the deck. This can be calculated as C(39, 1).
C(39, 1) = 39! / (1! * (39 - 1)!)
Now, to find the total number of ways to draw exactly 4 clubs and 1 non-club, we multiply the number of ways to choose 4 clubs by the number of ways to choose 1 non-club.
Total number of ways = C(13, 4) * C(39, 1)
Finally, we divide the total number of ways to draw 4 clubs and 1 non-club by the total number of ways to draw 5 cards to find the probability:
Probability = (C(13, 4) * C(39, 1)) / C(52, 5)
Calculate the values mentioned above to find the final probability.