To Activities

ISP 121 -- Activity 7

Probability and Risk

1. Suppose that 2% of the students at a particular college are infected with HIV.
   1. If a student has ten random sexual partners over a period of time, what is the probability that at least one of these partners is infected with HIV?

   2. If a student has twenty random sexual partners over a period of time, what is the probability that at least one partner is infected with HIV?

2. In 1953, French economist Maurice Allais studied how people assess risk. Here are two survey questions that he used:

   Decision 1

   Option A:  100% chance of gaining $1,000,000.

   Option B:  10% chance of gaining $2,500,000; 89% chance of gaining $1,000,000; and 1% chance of gaining nothing.

   Decision 2
   Option A:  11% chance of gaining $1,000,000 and 89% chance of gaining nothing.

   Option B:  10% chance of gaining $2,500,000 and 90% chance of gaining nothing.

   Which option would you select in each decision?

   Allais discovered that for decision 1, most people chose option A, while for decision 2, most people chose option B.

   1. For each decision, find the expected value of each option.

   2. Are the responses given in the surveys consistent with the expected values?

   3. Give a possible explanation for the responses in Allais' surveys.

3. In the "3 Spot" version of the former California Keno lottery game, a player picked three numbers from 1 to 40. Ten possible winning numbers were then randomly selected. It cost $1 to play. The table shows the possible outcomes.

   Number of Matches	Amount Won	Probability
   3	$20	0.012
   2	$2	0.137
   0 or 1	$0	0.851

   Compute the expected value for this game. Interpret what this expected value means.