Given the Venn Diagram with probabilities shown: Prob. Venn Diagram X Y 0.3 0.1 0.4 Find Pr( Not-X OR Not-Y). A. 0.1 B. 0.2 C. 0.3 D. 0.4.

A payoff table is given as    S1 S2 S3 D1 250 750 500 D2 300 -250 1200 D3 500 500 600 a. What choice should be made by the optimistic decision maker? b. What choice should be made by the conservative decision maker? c. What decision should be made under minimax regret? d. If the probabilities of d1, d2, and d3 are .2, .5, and .3 respectively, then what choice should be made under expected value?

1. Use this table for the following questions:                        Female      Male         TotalShort Hair       20              40             60 Long Hair        30              10             40 Total                50              50             100 a. Complete a total probability table.b. Complete a row probability tablec. Complete a column probability table.d. The probability that a student does not have long hair. _________e. The probability that a student is male or has short hair. ________f. The probability that a student is a female and has long hair. _________g. The probability that a student is male, given that the student has long hair. _________h. The probability that a student has long hair, given that the student is male. _________i. Of all the female students, the probability that a student has short hair. ________j. Of all students with long hair, the probability that a student is female. _________k. The probability that a student is female or has long hair.…