Answers Discrete distribution
1. We roll two dice and add up the sums of the numbers. Find the probabilities and expected value of the sums.
2. Lisa-Peter answered an exam with eight multiple-choice questions. She got one point for the correct answer and -0,5 points for the wrong answer. The questions had four possible answers, one of which was correct. Lisa-Peter answers the test by guessing. What is the expected value of her score?
Answer: The expected value for one question is -0.125 and the whole test is -1 point.
3. Marja-Unto played a game where four numbers out of ten were chosen. One round cost 2 euros. If she got all four right, she won 10 €. Three correctly won 5 euros. Two correctly won 2 euros and one got a euro. Calculate the expected value for the winning amount of one round.. Evaluate Marja-Unto's winning situation after a hundred rounds.
Answer: The expected value for one round is -0,14 € and after a hundred rounds the loss is 14 €.
4. In one computer game, the player advances to the top level according to the chart below and gets the score marked on the chart. At each intersection, he randomly selects one of the equal options and advances to the next level.
a) What is the probability that a player will achieve the highest score of 40?
b) Find the expected value of the score.
(YO2011S Long Mathematics)
Answer: a) P(40)=5/18 b) E(X)=25