Suppose we have an unfair coin such that heads is twice as likely to occur as tails (and no other outcomes are possible). To do this problem using the tools we have available to us right now, you need to figure out the probability of a head (using the axioms of probability) a) The probability of a head is (round to 4 decimals) To compute the probability of an outcome in a sample space, multiply the probabilities of each side being face up (for this to be true, the flips must be independent. We will discuss this in the "conditional probability" notes. You don't need to know this for this problem, I'm just mentioning it for later). For example, if there are 7 flips and the sequence of heads/tails is HHHTHTH, then the probability of this outcome is P(H)=P(H)*P(H)=P(T)=P(H)=P(T)*P(H). We will discuss this a lot more using the ideas of independence and distributions in the coming lectures. For now, answer these questions by writing down the sample space and identifying the outcomes that satisfy each event. Then use the probability identified in a) to answer the following three questions. b) If the coin is flipped 3 times, what is the probability of getting exactly 1 head? (round to 4 decimals) c)If the coin is flipped 5 times, what is the probability of getting exactly 2 tails? (round to 4 decimals) d) If the coin is flipped 4 times, what is the probability of getting at least 3 tails? (round to 4 decimals) Note: This should feel cumbersome and tedious. This is getting us warmed up to the idea of "distributions" which will make this calculation much faster