I don't understand how to approach the problem, should I use Bernoulli's formula?
You are asked to solve: In a game of A vs. B, player A tosses a coin twice whose probability of coming up heads is 1/4 and player B tosses a fair coin twice. The player who gets the most heads wins, if the number of heads matches it is considered a draw. -The probability that player B wins is: -The probability of a tie: -The probability that player A wins is:
First try to find probabilities of each possible outcome for one player at a time. That means $P[\text{player A gets 0 heads}]$, $P[\text{player A gets 1 heads}]$, $P[\text{player A gets 2 heads}]$ and likewise for player B.
Next, try to combine those probabilities. For example, what's the probability that A gets 1 heads and B gets 2 heads? Repeat this for the other combinations of how many heads each person obtains.
Finally, combine the results from the previous step. For example, A wins in the following cases: (A gets 1, B gets 0), (A gets 2, B gets 0), (A gets 2, B gets 1). So to get the probability of A winning, you need to sum up the probabilities of each of those 3 winning scenarios. To get the probability of a tie, you'd use the same method: List out the combinations of scores that create a tie, and then add up the probabilities of those combinations showing up. And likewise for B winning.
EDIT: In the comments, there was a followup question about how to compute $P(A gets 1 heads)$ and so on.
A's number of heads is a Binomial random variable with 2 trials and $p = 1/4$. B's number of heads is a Binomial random variable with 2 trials and $p = 1/2$. I recommend you should through that Wikipedia page and try to learn how to compute these probabilities. I think that will be more useful to your goals of learning about probability, compared to me just typing "the answer is that B wins with probability 52%" or whatever.