In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.




SAT Test When making a random guess for an answer to a multiple choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.

Verified step by step guidance

1. Step 1: Understand the problem. The question asks for the probability of correctly guessing the answer to a multiple-choice question with 5 possible answers (a, b, c, d, e).
2. Step 2: Recall the formula for probability. Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes. Mathematically, this is expressed as: $P=\frac{\mathrm{Favorable\; Outcomes}}{\mathrm{Total\; Outcomes}}$
3. Step 3: Identify the favorable and total outcomes. In this case, there is 1 favorable outcome (the correct answer) and 5 total possible outcomes (the 5 answer choices).
4. Step 4: Substitute the values into the probability formula. Using the formula from Step 2, substitute 1 for the favorable outcomes and 5 for the total outcomes: $P=\frac{1}{5}$
5. Step 5: Simplify the fraction if necessary. In this case, the fraction $\frac{1}{5}$ is already in its simplest form, so this represents the probability of correctly guessing the answer.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a value between 0 and 1. A probability of 0 indicates that the event cannot happen, while a probability of 1 indicates certainty. In the context of the SAT question, the probability of guessing the correct answer from five options is calculated as the number of successful outcomes (1 correct answer) divided by the total number of possible outcomes (5 options).

Random Guessing

Random guessing refers to making a choice without any knowledge or strategy, relying solely on chance. In the SAT example, when a student guesses an answer among five choices (a, b, c, d, e), each option has an equal likelihood of being selected. This concept is crucial for understanding how to calculate the probability of success when no prior knowledge influences the decision.

Multiple Choice Questions

Multiple choice questions present respondents with several answer options, from which they must select the correct one. The structure of these questions allows for straightforward probability calculations, as each option can be treated as an independent event. In the SAT scenario, knowing there are five choices helps in determining the probability of selecting the correct answer through random guessing.