Discrete MathA coin is flipped four times. For each of the events described below, express the event as a set in roster notation. Each outcome is written as a string of length 4 from {H, T}, such as HHTH. Assuming the coin is a fair coin, give the probability of each event.( a ) The first and last flips come up heads.( b ) There are at least two consecutive flips that come up heads.( c) There are at least two consecutive flips that are the same

Answer:a) 25%b) 50%c) 87.5%Step-by-step explanation:There are [tex]2^4 = 16[/tex] number of outcome in total. a)First and last flips come up heads. There are 4 outcomes here. Probability of the event is 4/16 = 1/4, or 25%.- HHHH- HHTH- HTHH- HTTHb) at least 2 Consecutive flips that is heads. There are 8 outcomes. Probability of event is 8/16 = 1/2, or 50%- HHHH- HHHT- HHTH- HHTT- THHH- THHT- HTHH- TTHHc) At least 2 consecutive flips that are the same. There are 14 outcomes. Probability of 14/16 = 7/8, or 87.5%- HHHH- HHHT- HHTH- HHTT- THHH- THHT- HTHH- TTHH- TTTT- TTTH- TTHT- HTTT- HTTH- THTT