1 pointA biased coin with probability of heads 0.750.75 is tossed three times. Let 𝑋X be a random variable that represents the number of head runs, a head run being defined as a consecutive occurrence of at least two heads. Then the probability mass function of 𝑋X is given by:𝑃(𝑋=𝑥)={0.375for 𝑥 = 00.625for 𝑥 = 1P(X=x)={ 0.3750.625​ for x = 0for x = 1​ 𝑃(𝑋=𝑥)={0.297for 𝑥 = 00.703for 𝑥 = 1P(X=x)={ 0.2970.703​ for x = 0for x = 1​ 𝑃(𝑋=𝑥)={0.016for 𝑥 = 00.140for 𝑥 = 10.422for 𝑥 = 20.422for 𝑥 = 3P(X=x)= ⎩⎨⎧​ 0.0160.1400.4220.422​ for x = 0for x = 1for x = 2for x = 3​ 𝑃(𝑋=𝑥)={0.016for 𝑥 = 00.844for 𝑥 = 10.140for 𝑥 = 2P(X=x)= ⎩⎨⎧​ 0.0160.8440.140​ for x = 0for x = 1for x = 2​

You toss a coin one time  1.  List the sample space __________   2. The number of events in the sample space is _________   3. The probability of getting 1 head is __________

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A coin is biased so that the probability it will come up tails is 0.46. The coin is tossed three times.  Consider a success to be tails.  Using the binomial probability formula, what is the probability the exactly two of the three tosses are tails?