Problem
You want to obtain cash by using an ATM, but it's dark and you can't see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first. Complete parts (a) through (c). a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The probability is $\frac{1}{4}$. (Type an integer or a simplified fraction.) B. This is a trick question. There is not enough information given to determine the answer. b. What is the probability of randomly selecting the card's position and finding that it is incorrectly inserted on the first attempt, but it is correctly inserted on the second attempt? (Assume that the same position used for the first attempt could also be used for the second attempt.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The probability is (Type an integer or a simplified fraction.) B. This is a trick question. There is not enough information given to determine the answer.
Solution
Step 1 ：The card can be inserted in four ways: front side up with the beginning of the name entering first, front side up with the end of the name entering first, back side up with the beginning of the name entering first, and back side up with the end of the name entering first. Only one of these ways is correct, so the probability of inserting the card correctly on a random attempt is 1 out of 4.
Step 2 ：The probability of selecting a random position and inserting the card with the result that the card is inserted correctly is \(\boxed{\frac{1}{4}}\).
