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Two surge protectors are connected to protect the television from damage due to voltage surges.

The probability that a surge protector will work is 0.985.

For computingthe probability of two events that occur simultaneously, the individual probabilities of the two events are multiplied, considering the interdependency of the events being studied.

Let A and B be the events that the first and second surge protector work correctly, respectively.

The probability that a surge protector will work correctly is given to be equal to 0.985.

Here, the probability that a surge protector will not work correctly is given by:

$$\begin{gathered} P\left(\stackrel{¯}{A}\right)=1-P\left(A\right) \\ =\left(1-0.985\right) \\ =0.015 \end{gathered}$$

$$\begin{gathered} P\left(\stackrel{¯}{B}\right)=1-P\left(B\right) \\ =\left(1-0.985\right) \\ =0.015 \end{gathered}$$

a.

In a series arrangement, the television would not get damaged by a voltage surge if at least one of the two surge protectors works.

Three cases are possible:

$$\begin{gathered} P\left(AandB\right)=0.985×0.985 \\ =0.970225 \end{gathered}$$

$$\begin{gathered} P\left(Aand\stackrel{¯}{B}\right)=0.985×0.015 \\ =0.14775 \end{gathered}$$

$$\begin{gathered} P\left(\stackrel{¯}{A}andB\right)=0.015×0.985 \\ =0.14775 \end{gathered}$$

The probability that the television will not get damaged due to a voltage surge if both the surge protectors are connected in series is the sum of the above three probabilities, and is given by:

$$\begin{gathered} P\left(nodamage\right)=0.970225+0.14775+0.14775 \\ =0.999775 \end{gathered}$$

Therefore, the probability that the television will not get damaged due to a voltage surge if both the surge protectors are connected in series is equal to 0.999775.

b.

In a parallel arrangement, the television would not get damaged by a voltage surge if both the surge protectors work.

The probability that both the surge protectors will work is given by:

$$\begin{gathered} P\left(AandB\right)=0.985×0.985 \\ =0.970225 \end{gathered}$$

Therefore, the probability that the television will not get damaged due to a voltage surge if both the surge protectors are connected in parallel is equal to 0.970225.

c.

The arrangement which provides a greater probability of protecting the TV from voltage surge is regarded better.

As the probability of no damage to the television is high in the case of series arrangement (0.999775) as compared to the parallel arrangement (0.970225), the series arrangement is a better option for the protection of the television from a voltage surge