5. An FBI survey shows that about 20% (i.e., 0.2) of all property crimes go solved. Suppose that in your city 13 such crimes are committed and they are each deemed independent of each other. a. What is the probability that exactly 3 of these 13 crimes will be solved? b. What is the probability that at most 3 of these 13 crimes will be solved? c. What is the probability that more than 11 of these 13 crimes will be solved?

X Y 0 0 1 7 2 14 3 21

Your friend makes up a game to play over Zoom during the shelter in place, and asks if you would like to play.  The rules are: You win $8 if you roll a 6. You win $4 if you roll a 4 or 5 Otherwise, you have to pay $10. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. The first value is filled in for you.  Round to 4 decimal places where appropriate.  Probability Distribution Table X P(X) -10           b. Find the expected profit. $ (Round to the nearest cent)c. Interpret the expected value. You will win this much if you play a game. This is the most likely amount of money you will win. If you play many games, on average, you will likely win, or lose if negative, close to this amount.