Question

There are twelve engines. Each engine can either be on or off chosen at random. 1....

There are twelve engines. Each engine can either be on or off chosen at random.

1. What is the probability that at least two are on.

2. What is the probability that at least one is on.

(Answer in a fraction.)

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Let be the random variable which represents the number of engines that are on.

Clearly as given, a engine has two states on or off chosen at random. Therefore the probability that system is on is .

More over, the number of system is also given i.e.=.

Using all this information, we have

.

The probability distribution function of is given by the equation below.

1. The probability that atleast 2 are on=

2. The probability that atleast one is on=

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