Question

Online chat rooms allow people from all over the world to exchange opinions on various topics of interest. A side effect of such conversations is "flaming," which is negative criticism of others' contributions to the conversation. A paper investigated the effect that personal criticism has on an individual. Data from a survey of 195 chat room users from this study are summarized here.

	Have Been Personally Criticized	Have Not Been Personally Criticized	Total
Have Criticized Others	19	9	28
Have Not Criticized Others	23	144	167
Total	42	153	195

Assume that this data is representative of the larger group of all chat room users and that the frequencies in the table are indicative of the long-run behavior of chat room users. Suppose that a chat room user is selected at random, and define events given below.

• C = event that the selected individual has criticized others
• O = event that the selected individual has been personally criticized by others

Find and interpret each of the following probabilities.

(a)

Find

P(C).

(Round your answer to three decimal places.)Interpret

P(C).

The percent of chat room users that have criticized others and have been personally criticized.The percent of chat room users who have been personally criticized that have criticized others.    The percent of chat room users who have personally criticized others that have been personally criticized.The percent of chat room users that have criticized others.The percent of chat room users that have been personally criticized.

(b)

Find

P(O).

(Round your answer to three decimal places.)Interpret

P(O).

The percent of chat room users that have criticized others and have been personally criticized.The percent of chat room users who have been personally criticized that have criticized others.    The percent of chat room users who have personally criticized others that have been personally criticized.The percent of chat room users that have criticized others.The percent of chat room users that have been personally criticized.

(c)

Find

P(C ∩ O).

(Round your answer to three decimal places.)Interpret

P(C ∩ O).

The percent of chat room users that have criticized others and have been personally criticized.The percent of chat room users who have been personally criticized that have criticized others.    The percent of chat room users who have personally criticized others that have been personally criticized.The percent of chat room users that have criticized others.The percent of chat room users that have been personally criticized.

(d)

Find

P(C|O).

(Round your answer to three decimal places.)Interpret

P(C|O).

The percent of chat room users that have criticized others and have been personally criticized.The percent of chat room users who have been personally criticized that have criticized others.    The percent of chat room users who have personally criticized others that have been personally criticized.The percent of chat room users that have criticized others.The percent of chat room users that have been personally criticized.

(e)

Find

P(O|C).

(Round your answer to three decimal places.)Interpret

P(O|C).

The percent of chat room users that have criticized others and have been personally criticized.The percent of chat room users who have been personally criticized that have criticized others.    The percent of chat room users who have personally criticized others that have been personally criticized.The percent of chat room users that have criticized others.The percent of chat room users that have been personally criticized.

Answer 1

a)

P(C) =28/195 =0.144

The percent of chat room users that have criticized others.

b)

P(O) =42/195 =0.215

.The percent of chat room users that have been personally criticized.

c)

P(C ∩ O)=19/195=0.097

The percent of chat room users that have criticized others and have been personally criticized.

d)

P(C|O)=19/42 =0.452

The percent of chat room users who have personally criticized others that have been personally criticized

e)

P(O|C) =19/28 =0.679

.The percent of chat room users who have been personally criticized that have criticized others