Question

1- A particular automatic sprinkler system has two different types of activation devices for each sprinkler head. One type has a reliability of 0.87; that is, the probability that it will activate the sprinkler when it should is 0.87. The other type, which operates independently of the first type, has a reliability of 0.77. If either device is triggered, the sprinkler will activate. Suppose a fire starts near a sprinkler head.

a) What is the probability that the sprinkler head will be activated?

b) What is the probability that the sprinkler head will not be activated?

c) What is the probability that both activation devices will work properly?

d) What is the probability that only the device with reliability 0.87 will work properly?

2-A computer password consists of six characters.

a) How many different passwords are possible if each character may be any lowercase letter or digit? Please enter your result in scientific notation, making sure the answer in the left box is between 1 and 10.

(----------) × 10⁹

b) How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? Please enter your result in scientific notation, making sure the answer in the left box is between 1 and 10.

(-----------) x 10⁹

c) A computer system requires that passwords contain at least one digit. If six characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits, what is the probability that a valid password will be generated?

Answer 1