In given problem, are "dividends paid" and "price increase" independent events?
Problem
An investment analyst collects data on stocks and notes whether or not dividends were paid and whether or not the stocks increased in price over a given period. Data are presented in the following table.
|
|
Price Increase
|
No Price Increase
|
Total
|
|
Dividends paid
|
34
|
78
|
112
|
|
No dividends paid
|
85
|
49
|
134
|
|
Total
|
119
|
127
|
246
|
a. If a stock is selected at random out of the analyst's list of 246 stocks, what is the probability that it increased in price?
b. If a stock is selected at random, what is the probability that it paid dividends?
c. If a stock is randomly selected, what is the probability that it both increased in price and paid dividends?
d. What is the probability that a randomly selected stock neither paid dividends nor increased in price?
e. Given that a stock increased in price, what is the probability that it also paid dividends?
f. If a stock is known not to have paid dividends, what is the probability that it increased in price?
g. What is the probability that a randomly selected stock was worth holding during the period in question; that is, what is the probability that it increased in price or paid dividends or did both?