Final answer:
To find the actual amount Peter made per turn in the Star One lottery, we need to calculate his expected gain or loss. The probability of both his letter and digit matching the ones picked on that day is 1/260. By finding the expected value of X, we can determine that Peter made -$3.0192 per turn. The correct answer is A. -$4.50.
Step-by-step explanation:
To find the amount Peter made per turn, we need to calculate his expected gain or loss. Let's start by finding the probability of both his letter and digit matching the ones picked on that day. There are 26 letters from A to Z and 10 digits from 0 to 9, so there are 26 * 10 = 260 possible combinations. Only one of these combinations will match the ones picked on that day, so the probability is 1/260.
Next, we need to calculate the expected value of X. The expected value is given by the sum of each possible outcome multiplied by its probability. In this case, the possible outcomes are winning $700 or losing $3. The probability of winning is 1/260, and the probability of losing is 259/260. Therefore, the expected value is (1/260) * 700 + (259/260) * (-3) = -0.0192.
Since Peter buys one ticket for $3, his actual amount made per turn is -$3 + (-0.0192) = -$3.0192.
Therefore, the correct answer is A. -$4.50.