77 54. cos cos T +

At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time? (4) (0.32) (0.68) 1! 4! (0.32)¹ (0.68)³ O2(0.32)(0.68) (0.32) (0.68)³

Suppose your school has 1000 students. Why can you be pretty sure that some pair of them will have telephone numbers that end in the same two digits and that they will like the same brand of soda?

There is an island where all people either always lie, or always tell the truth. You meet D who says "I am lying." What can you deduce?

Unfortunately, for some reason, at least one of the answers isn't correct. I got the same answeres myself. Is there a reason any could be wrong?

Are these true or false and why?

What is the “method of false position”, and how does it work?