Under an insurance policy, a maximum of five claims may be filed per year by a policyholder. Let Pn be the probability that a policyholder files n claims during a given year, where n 0,1,2,3,4,5. An actuary makes the following observations: i) Pn≥ 2pn+1 for n= 0, 1,2, 3,4
ii) The difference between pn and pn+1 is the same for n 0,1,2, 3,4
iii) Exactly 40% of policyholders file fewer than two claims during a given year Calculate the probability that a random policyholder will file more than three claims during a given year.
A) 0.14
B) 0.16
c) 0.27
D) 0.29
E) 0.33

Through non-collinear points there is exactly one plane.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.