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You are developing an online service for a bank. To make use of this service, the customers of the bank will be required to associate their username to a passcode. The passcode will have to be 4-digit long and will have to be made of digits in the range 0-9. You are considering whether repetitions should be allowed or not. Option A is to require users a 4-digit code in which repetitions are allowed. Option B is to require users a 4-digit code in which repetitions are not allowed. In which of Options A and B the passcode is less likely to be guessed at random? Both systems are equally safe System A O System B At the amusement park they have a game where you can pick a rubber duck out of a pool and win the prize at the bottom of the duck. There are 35 ducks in the pool: . 20 of the ducks have no prize 7 have a prize of $1 4 have a prize of $2 . 3 have a prize of $5 1 has a $10 prize. First, suppose that you play one time: - What is the probability that if you play, you win at least $2? [Select] - If you pay $2 to play, what is your expected net gain? (Note: a negative gain indicates a loss) [Select] - What should be the cost of playing the game for your expected net gain to equal $0.33? [Select] Now, suppose you and your friend Qi are both going to play the game. Each time that the game is played there are the same 35 rubber ducks in the pool. What is the probability that both of you pick one of the ducks with no prize? [Select] What is the probability that at least one of you picks one of the ducks with a $5 prize? Select]