3. A new cold medication was tested by giving 125 people the drug and 100 people a placebo. A control group consisted of 115 people who were given no treatment. The number of people in each group who showed improvement is shown in the table below.

Cold drug Placebo Control total

Improvement 72 55 38 165

No improvement 53 45 77 175

Total 125 100 115 340

a) What is the probability that a randomly selected person in the study either was given the placebo or was in the control group?____________

b) What is the probability that a randomly selected person either was given the drug or improved? _____________

c) What is the probability that a randomly selected person was given the drug and improved? ______________

d) What is the probability that a randomly selected person who improved was given the drug? ________

e) What is the probability that a randomly selected person who was given the drug improved? ________

f) Based on these data, does the drug appear to be effective? ____________

Expected Value - The theoretical value for you, the player in a game, is calculated as follows: If an outcome results in a win for you, multiply its probability by the profit you win. If an outcome results in a loss for you, multiply the probability by the negative of the amount you lose. Your expected value is the sum of all these positive and negative numbers. A simplified formula for this is

Expected value = P(Win) x Profit - P(Lose) x Loss

The expected value is a measure of the average amount you can expect to win (or lose) per play in the long run.

If the expected value is zero, the game is fair.