1. If you roll a fair 12-sided dice one time (each number between 1 and 12 is equally likely to be the result), what is the probability that the result will be less than () 10?

1. If you draw a random card from a standard deck of playing cards, the probability that your card will be a King is 1/13 = 0.0769. If you put your card back into the deck and shuffle the cards before drawing a random card again, the probability that your card will be a King is still 1/13 = 0.0769. If you repeat this process ten times, what is the probability that you will draw a King exactly two times out of ten?

The following table shows the distribution of annual income-s earned by current participants in a certain multilevel marketing firm. The relative frequencies of all but one category are displayed above the number of people in each category. What is the probability that a randomly selected participant in this rm is making zero dollars? Distribution of Incomes 555.3251); 7-10 Refer to the following scenario: Ind. Flintstone has just bought a new car. As a reasonably safe driver, they believe that there is only a 5% chance of being in an accident in the forthcoming year. If they are involved in an accident, the damage to their new car depends on the severity of the accident. Ind. Flintstone is trying to decide whether they are willing to pay $2000 for collision insurance with a $300 deductible (note that with this type of insurance, they pay the first $300 in damages and the insurance company pays the rest). Let us also assume that if Ind. Flintstone knows they don't have insurance, they will drive in such a way as to lower the probabilities that an accident will be Serious or Catastrophic. The decision tree below represents Ind. Flintstone's decision and potential costs. I've listed these as negative values to highlight the fact that these are costs. Minor -$200 Moderate -$300 Accident 5% Serious -$300 B 95% Catastrophic -$300 Buy Insurance No Accident -$2000 A Minor -$200 I Don't Buy Accident Moderate -$1,000 5% C Serious -$4,000 95% Catastrophic -$30,000 No AccidentA Don't Buy Minor -$200 Accident 5% Moderate -$1,000 Serious -$4,000 95% No Accident Catastrophic -$30,000 7. If Ind. Flintstone employs an optimistic strategy, what will be the value of node D? 8. If Ind. Flintstone employs a conservative strategy, what will be the value of node C? 9. How much regret would Ind. Flintstone feel (in terms of dollars) if they do not buy insurance and then experience a moderate accident? 10.If Ind. Flintstone employs an expected-cost minimization strategy, what will be their optimal decision? Why