40% of the Adult Residents of a Certain City Own

Essay

40% of the adult residents of a certain city own their own home. Four residents are selected at random from the city and asked whether or not they own their own home. Considering a success to be "owns their own home", formulate the process of observing whether each of the four residents owns their own home as a sequence of four 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 four residents own their own home. Without using the binomial probability formula, find the probability that exactly two of the four residents own their own home. $$\begin{array} { r | r } \text { Outcome } & \text { Probability } \\ \hline \operatorname { ssss } ( 0.4 ) ( 0.4 ) ( 0.4 ) ( 0.4 ) = 0.026 \end{array}$$