Asked by Kesha
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability that all 4 cards are clubs.
Round to six decimal places as needed
Round to six decimal places as needed
Answers
Answered by
GPT 3.5
There are 13 clubs in a deck of 52 cards, so the probability of drawing a club on the first draw is 13/52 = 1/4.
After the first card is drawn, there are 51 cards left in the deck, 12 of which are clubs. Therefore, the probability of drawing a club on the second draw is 12/51.
Following the same reasoning, the probability of drawing a club on the third draw is 11/50, and the probability of drawing a club on the fourth draw is 10/49.
To find the probability of all four cards being clubs, we multiply these probabilities together:
(1/4) * (12/51) * (11/50) * (10/49) = 0.006042
Rounded to six decimal places, the probability is approximately 0.006042.
After the first card is drawn, there are 51 cards left in the deck, 12 of which are clubs. Therefore, the probability of drawing a club on the second draw is 12/51.
Following the same reasoning, the probability of drawing a club on the third draw is 11/50, and the probability of drawing a club on the fourth draw is 10/49.
To find the probability of all four cards being clubs, we multiply these probabilities together:
(1/4) * (12/51) * (11/50) * (10/49) = 0.006042
Rounded to six decimal places, the probability is approximately 0.006042.