Ten cards are selected without replacement from a standard 52 card deck that contains 13 clubs and 39 other cards. What is the probability
that 4 of them are clubs?
this is a combination question since the order does not matter
Prob(4clubs out of 10cards)
= C(13,4)*C(39,6)/C(52,10)
= 715(3262623)/(1.582x10^10)
= .1475
let me know if my choice of C(n,r)'s don't make sense to you.
your doing independent event is different from my math class i don't get it my got different from ur math hmmmm
To find the probability that 4 of the selected cards are clubs, we need to calculate the number of favorable outcomes (4 clubs) divided by the total number of possible outcomes.
Let's first find the total number of possible outcomes. We are selecting 10 cards without replacement from a standard 52 card deck, so the total number of possible outcomes is given by the combination formula:
Total number of possible outcomes = C(52, 10) = 52! / (10! * (52-10)!)
Now, we need to find the number of favorable outcomes. In this case, we want exactly 4 cards to be clubs. We can calculate this as follows:
Number of ways to choose 4 clubs from 13 = C(13, 4) = 13! / (4! * (13-4)!)
Since we are selecting 4 clubs from 13 and there are 39 non-club cards remaining, we'll need to choose additional 6 cards from the 39 non-club cards.
Number of ways to choose 6 non-club cards from 39 = C(39, 6) = 39! / (6! * (39-6)!)
To find the total number of favorable outcomes, we need to multiply these two quantities:
Number of favorable outcomes = [C(13, 4)] * [C(39, 6)]
Finally, to calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Now you can substitute the values into the formula to find the probability.