Trying to understand a probability question

Question

I'm trying to understand a probability question regarding a biased coin, not quite sure how to factor in the biased probability in the question, and also I wanted to make sure the answer is correct, as I think the lecturer might have made a mistake in one of them, which could possibly throw off everything else, and I don't know if it's just me being stupid.

Here is the question:

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1.) A biased coin is flipped 4 times. The probability of the coin showing 'heads' is p = 3/4. Answer the following questions.

a) What is the probability that exactly 3 flips show 'heads'? Answer: $\frac{27}{60}$

b) What is the probability that at least three flips show heads? Answer: $\frac{189}{256}$

c) Given that three flips show 'heads' what is the probability that the last flip was a 'head'? Answer: $\frac{3}{4}$

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The only one I understand is the last one, unless a) presents an incorrect answer, then I understand that, because the answer I get is $\frac{27}{64}$

So in short, I'd like to know how to do these types of questions, where it factors bias elements.

Answer 1

This is based on Binomial distribution.

1 a) your answer is correct, likely a typo in the solution cited.

Answer 2

You will need the binomial distribution for this one.

Hints:

The coin flips can be treated as independent.

The heads and tails can be in any order, so you have to count how many ways they can be ordered.