2.63 According to Consumer Digest (July/August 1996), the probable location of personal computers (PC) in the home is as follows: Adult bedroom: 0.03 Child bedroom: 0.15 Other bedroom: 0.14 Office or den: 0.40 Other rooms: 0.28 (a) What is the probability that a PC is in a bedroom? (b) What is the probability that it is not in a bedroom? (c) Suppose a household is selected at random from households with a PC; in what room would you expect to find a PC?

a) 0.32

b) 0.68

c) office or den

Step-by-step explanation:

Locations Probabilities

Adult bedroom 0.03

Child bedroom 0.15

Other bedroom 0.14

Office or den 0.40

Other rooms 0.28

a)

P (PC in bedroom) = P (PC in adult bedroom) + P (PC in child bedroom) + P (PC in other bedroom)

P (PC in bedroom) = 0.03+0.15 + 0.14

P (PC in bedroom) = 0.32.

Thus, the probability that a PC is in a bedroom is 0.32.

b)

P (PC is not in bedroom) = P (PC in Office or den) + P (PC in Other rooms)

P (PC is not in bedroom) = 0.40+0.28

P (PC is not in bedroom) = 0.68.

Thus, the probability that a PC is not in a bedroom is 0.68.

c)

When a household is selected at random from households with a PC we would expect to find a PC in a room which has a greater probability of having PC.

The greater probability of room having a PC is of Office or den room with probability 0.40. So, when a household is selected at random from households with a PC we would expect to find a PC in a Office or den room.