4. Probability

Counting

4. Probability

Counting

2:02 minutes

Problem 4.4.24c

Textbook Question

ATM 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.

c. How many random selections are required to be absolutely sure that the card works because it is inserted correctly?

Verified step by step guidance

Understand the problem: The card can be inserted into the ATM in four possible orientations. Only one of these orientations is correct, where the front side is up and the beginning of the name enters first.

List all possible orientations: (1) Front side up, name first (correct orientation), (2) Front side up, name last, (3) Back side up, name first, (4) Back side up, name last.

Recognize that to be absolutely sure the card works, you must test all four possible orientations, as there is no way to know in advance which one is correct.

Conclude that the number of random selections required to guarantee the correct orientation is equal to the total number of possible orientations, which is 4.

Verify the reasoning: Since there are 4 orientations and only one is correct, testing all 4 ensures that the correct orientation is eventually tested.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Random Selection

Random selection refers to the process of choosing items or options in such a way that each has an equal chance of being selected. In the context of the ATM card, it implies that you might need to try different orientations of the card to ensure it is inserted correctly. Understanding this concept is crucial for determining the number of attempts needed to guarantee success.

Permutations

Permutations are arrangements of objects in a specific order. For the ATM card, the orientation and order of insertion (front side up and name first) create different permutations. Knowing how to calculate permutations helps in understanding the total number of possible ways the card can be inserted, which is essential for determining how many attempts are necessary.

Probability

Probability is the measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this scenario, understanding the probability of successfully inserting the card correctly on the first try is important. This concept helps in assessing how many random selections might be needed to ensure that the card works, given the various possible orientations.

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Textbook Question

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Textbook Question

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a. How many different ways can the five officers be appointed?

Textbook Question

b. How many different ways can a committee of five be appointed?

Textbook Question

ATM 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.

a. What is the probability of selecting a random position and inserting the card with the result that the card is inserted correctly?

Textbook Question

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a. If 20 newborn babies are randomly selected, how many different gender sequences are possible?

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a. What is the probability of randomly generating 16 digits and getting your MasterCard number?

Textbook Question

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Textbook Question

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