Question

you want to obtain cash by using an atm, but its dark and you cant 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 cards 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.

Explanation:

Step1: Analyze correct - insertion probability

There are 4 possible orientations of the card (front - up with name - first, front - up with name - last, back - up with name - first, back - up with name - last). Only 1 is correct. So the probability of correct insertion on a single random try is $\frac{1}{4}$.

Step2: Analyze incorrect - then - correct insertion probability

The probability of incorrect insertion on the first try is $1-\frac{1}{4}=\frac{3}{4}$. The probability of correct insertion on the second try is $\frac{1}{4}$. Since these are independent events, the probability of incorrect insertion on the first try and correct insertion on the second try is $\frac{3}{4}\times\frac{1}{4}=\frac{3}{16}$.

Answer:

a. A. The probability is $\frac{1}{4}$
b. A. The probability is $\frac{3}{16}$