Miss Leo buys one mini lottery everyday. For every lottery she buys, it costs $1 and it has 0.001 to win the prize with value $200. (a) Miss Leo starts buying the lottery since Day 1. Let N be the first day(counting from Day 1) she wins the lottery. What is the distribution of N? Specific the parameter. Find also the expected value of N. (b) Let X be the count of lotteries that won by Miss Leo in two years (2 × 365 = 730 days). Explain why X can be approximated as a Poison random variable. Specify the parameter (i.e., the rate) of the Poison distribution. (c) Use the approximation from (b) to estimate the probability that Miss Leo wins > 1 lottery in two years. (d) Let Z be the net profit after two years (the difference of the total prize she earns and the total cost of lotteries). Find E [Z].

Sick leave probability that a given worker at Dyno Nutrition Will call in sick on a Monday is 004. The packaging department has eight workers. What is the probability that two or more ackaging workers Will call in sick next Monday ?

Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an $8000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning (and that of B winning) if the game were to continue? The French mathematicians Pascal and Fermat corresponded about this problem, and both came to the same correct conclusion (though by very different reasoning's). Their friend Roberval disagreed with both of them. He argued that player A has probability of Winning, because the game can end in the four ways H, TH, TTH, TTT, and in three of these, A wins. Roberval’s reasoning was wrong. Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform this experiment 80 or more times, and estimate the probability that player A wins. Calculate the probability that player A wins. Compare with your estimate from part (a).

Determine if the statement is true or false. If the statement is false, then correct it and make it true. The probability that an event occurs can be a negative number.