The probability of Pick 3 lottery games

1. In a state's Pick 3 lottery game, you pay $1.22 to select a sequence of three digits, such as 700. If you select the same sequence of three digits that are drawn, you win and collect $434.58.
a. How many different selections are possible?
b. What is the probability of winning? (Integer or a decimal)
c. If you win, what is your net profit? (Integer or a decimal)l)
c. If you win, what is your net profit?
d. Find the expected value (Round to the nearest hundredth as needed)
e. If you bet $1.22 in a certain state's Pick 4 game, the expected value is $0.79. Which bet is better, a $1.22 bet in the Pick 3 game or a $1.22 bet in the Pick 4 game? Explain.
a. The pick 3 game is a better bet because it has a larger expected value.
b. Neither bet is better because both games have the same expected value.
c. The pick 4 game is a better bet because it has a larger expected value.

2. Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean u and standard deviation o. Also, use the range rule of thumb to find the minimum usual value U - 2o and the maximum usual value u + 2o

n = 1490, p 4/5

u =
o = (Round to one decimal place as needed)
u - 2o = (Round to one decimal place as needed)
u + 2o = (Round to one decimal place as needed)

3. A government agency has specialists who analyze the frequencies of the letters of the alphabet in an attempt to decipher intercepted messages. In standard English text, a particular letter is used at a rate of 5.7%
a. Find the mean ans standard deviation for the number of times this letter will be found on a typical page of 2600 characters
u =
o = (Round to one decimal place as needed)

b. In an intercepted message, a page of 2600 characters is found to have the letter occurring 168 times. Is this unusual?
a. Yes, because 168 is below the minimum usual value
b. Yes, because168 is greater than the maximum usual value
c. No, because 168 is within the range of usual values
d. Yes, because 168 is within the range of usual values.