Question: Often it is difficult to distinguish between the probability of an intersection of outcomes (joint probability) and the probability of a conditional outcome (conditional probability). Classify the following as joint probability statements or conditional probability statements. [If in doubt, try to write down the probability statement; for example, P(Crash Landing | Out of Fuel) or P(Dow Jones Up and Stock Price Up).]
a. Eight percent of the students in a class were left-handed and red-haired.
b. Of the left-handed students, 20% had red hair.
c. If the Orioles lose their next game, then the Cubs have a 90% chance of winning the pennant.
d. Fifty-nine percent of the people with a positive test result had the disease.
e. For 78% of patients, the surgery is a success and the cancer never reappears.
f. If the surgery is a success, the cancer is unlikely to reappear.
g. Given the drought, food prices are likely to increase.
h. There is an even chance that a farmer who loses his crop will go bankrupt.
i. If the temperature is high and there is no rain, farmers probably will lose their crops.
j. John probably will be arrested because he is trading on insider information.
k. John probably will trade on insider information and get caught