Question

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).

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Part 1
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

enter your response here.
​(Type an integer or a simplified​ fraction.)
B.
This is a trick question. There is not enough information given to determine the answer.
Part 2
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

4.83.
​(Type an integer or a simplified​ fraction.)
B.
This is a trick question. There is not enough information given to determine the answer.
Part 3
c. How many random selections are required to be absolutely sure that the card works because it is inserted​ correctly? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The number of random selections required is

enter your response here.
​(Type an integer or a simplified​ fraction.)
B.
This is a trick question. There is no finite number of​ attempts, because it is possible to get the wrong position every time.

Answer 1

a. The probability of selecting a random position and inserting the card correctly on the first attempt is 1/2 or 50% since there are only two possible ways to insert the card and only one of them is correct.

b. The probability of the card being incorrectly inserted on the first attempt and correctly inserted on the second attempt is (1/2) * (1/2) is 1/4 or 25%.

c. The number of random selections required to be sure that the card works because it is inserted correctly is 2 attempts.

a) The number of ways to insert the card correctly = 1

The number of ways to insert the card incorrectly = 1

The sum of ways to insert the card = 2

The probability of inserting it correctly = 1/2

b) The probability of inserting the card incorrectly on the first attempt is 1/2.

With the second attempt, the probability of inserting it correctly is also 1/2.

Thus, the probability of the card being incorrectly inserted on the first attempt and correctly inserted on the second attempt is (1/2) * (1/2) = 1/4.

c) To be sure that the card works because it is inserted correctly, you would need to make 2 attempts.

The chance of inserting the card correctly on the first attempt = 1/2

The chance of inserting the card correctly on the second attempt = 1/2

After 2 attempts, you can be sure that the card is inserted correctly.