A Coin Is Biased So That the Probability It Will $\begin{array} { r | r } \text { Outcome } & \text { Probability } \\ \hline \operatorname { hhh } & ( 0.57 ) ( 0.57 ) ( 0.57 ) = 0.185 \end{array}$

question 97

Essay

A coin is biased so that the probability it will come up tails is 0.43. The coin is tossed three times. Considering a success to be tails, formulate the process of observing the outcome of the three tosses as a sequence of three Bernoulli trials. Complete the table below by showing each possible outcome together with its probability. Display the probabilities to three decimal places. List the outcomes in which exactly two of the three tosses are tails. Without using the binomial probability formula, find the probability that exactly two of the three tosses are tails.
$\begin{array} { r | r } \text { Outcome } & \text { Probability } \\ \hline \operatorname { hhh } & ( 0.57 ) ( 0.57 ) ( 0.57 ) = 0.185 \end{array}$

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