Math Help - Probability of compound events?

1. Probability of compound events?

I am having difficulty with these two questions

1. The probability of at least 4 tails facing up when 6 coins are dropped on the floor.

2. Find probability using standard deck of cards

P(both king or aces) if two cards are drawn without replacement.

I know there are 8 aces and kings in 52 card deck but I am confused on how to set problem up I think it mutually inclusive.

2. Re: Probability of compound events?

Originally Posted by homeylova223
1. The probability of at least 4 tails facing up when 6 coins are dropped on the floor.
With six coins the probability of any given event is $\frac{1}{2^6}$.

Now all you need do is answer "how many ways can we arrange $TTTTHH~?$

3. Re: Probability of compound events?

Hmm I am not sure how many way to arrange 4 Tails and two heads. I am slightly confused on that part would you just do 6 ncr 4?

4. Re: Probability of compound events?

Originally Posted by homeylova223
Hmm I am not sure how many way to arrange 4 Tails and two heads. I am slightly confused on that part would you just do 6 ncr 4?
Yes $\binom{6}{4}$.

5. Re: Probability of compound events?

If 6 ncr 4 equals 15

Would the final answer just be (15/(1/2^6) or is there an extra step I am missing

6. Re: Probability of compound events?

Originally Posted by homeylova223
If 6 ncr 4 equals 15
Would the final answer just be (15/(1/2^6) or is there an extra step I am missing
Well almost: $\frac{15}{2^6}$ is the final answer.