Please help to solve the problems related to probability, gambling game ...etc, thank you very much

 

1.A small delegation of k students is chosen by lot (at random) from a class of size n tocomplain about a certain aspect of the course . Assume Flora and Mike are in the classand that 1<k<n.a.Is the probability that Mike is in the delegation 1/k, 1/n, or something else?b.What is the probability that Flora is in the delegation?c.Are the events “Mike is in” and “Flora is in “independent?2.A die is weighted so thata 3 comes up 7 times as often as 4b 4 comes up twice as often as 1, 2, 5. And 6c 1, 2, 5, and 6 are equally likelyLet X denote that outcome of any roll and let q=P(X=4).Part1: Determine the probability distribution for X and the value for qPart2: Find E(X), the expected value of X.3.A bank “password” is a sequence of 4 digits. If passwords were generated at random,what would be the expected number of 5’s?4.It is known that 85% of individuals who purchase a make of laptop do not make anyclaims on their guarantee. Suppose 43 customers buy that make of laptop. Computer theprobability that at least three owners will make a claim on their guarantee.5.Suppose that in a certain board game player A will win if she rolls a 4 on either or both oftwo unbiased dice.A What is the probability that she will win on her next roll?B How many rolls should she expect to roll until she wins?6.Imagine a gambling game played with an ordinary deck of 52 cards. You pay $2.5 to playand you play by shuffling the deck and then turning over the top cardIf the top card is a diamond, you win $4.5If the top card is a picture (face) car, you win $4.5, but J, Q or K of diamonds wins$7.00If the top card is an ace, you win $5.00, but the ace of diamonds win $10.00If the top card is a any other card, you win nothingQ1: let f be your payoff, that is your win minus the $2.5, then f has a value for every cardturned up, but only has 5 different values. Determine the probability distribution for thesevalues.Q2: Calculate the expected value for f.Q3 Why is the average payoff per play negative?

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• 1492959426-problem set5-probalityy.docx