Probability Problem - Check if I am right?

Question

I am currently working on a probability question and was wondering if I am doing it right.

(a) Suppose you flip 4 coins. Flips are independent, with the probability of heads being 0.5 for each flip. Find the probability that at least two flips land on heads.

My Answer

1. Find the complement: P(0 or 1 flips land on heads out of the 4)
2. Use combinations: 0 heads = 4C0 = 1 | 1 head = 4C1 = 4. 4 + 1 = 5
3. There are 5/16 chances that we get 0 or 1 head in 4 flips
4. Switch back over: 1 - (5/16) = .6875 chance at least 2 of the 4 flips land heads

(b) Find the conditional probability that all four flips land heads given that at least $\color{red}{two}$ flips land heads.

My Answer

1. Create conditional: P(4 flips land heads) = P(A). P(at least 2 flips land heads) = P(B). We are looking for P(A | B)
2. P(A | B) = P(A intersection B) / P(B)
3. Plug in values: P(A intersection B) = P({H, H, H, H}) = (1/2)^4 = .0625. P(B) = .6875.
4. .0625 / .6875 = .090909 = 9.09% is the probability that if you land at least 2 heads, you will flip all heads.

Is this right?