Question:Exercise 17.26What probability doesn't say. The probability of a head in tossing a coin is 1/2. This means that as we make more tosses, the proportion of heads will eventually get close to 0.5. It does not mean that the count of heads will get close to 1/2 the number of tosses. To see why, imagine that the proportion of heads is 0.49 in 100 tosses, 0.493 in 1000 tosses, 0.4969 in 10,000 tosses, and 0.49926 in 100,000 tosses of a coin. How many heads came up in each set of tosses? How close is the number of heads to half the number of tosses?

Exercise 18.12 Roulette. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black. The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors.

(a)What is the probability of any one of the 38 possible outcomes? Explain your answer.

(b)If you bet on "red," you win if the ball lands in a red slot. What is the probability of winning?

(c)The slot numbers are laid out on a board on which gamblers place their bets. One column of numbers on the board contains all multiples of 3, that is, 3, 6, 9,, 36. You place a "column bet" that wins if any of these numbers comes up. What is your probability of winning?