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Chapter 4: Problem 6

"Who discovered penicillin: Sean Penn, William Penn. Penn Jillette, Alexander Fleming, or Louis Pasteur?" If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Alexander Fleming?

Short Answer

Expert verified
The probability of selecting Alexander Fleming's name randomly is \[\frac{1}{5}\].

Step by step solution

01

List All Possible Answers

Start by listing all the given options: Sean Penn, William Penn, Penn Jillette, Alexander Fleming, and Louis Pasteur. Count the total number of possible answers.
02

Identify the Correct Answer

Determine which of the listed answers is correct. The problem states that the correct answer is Alexander Fleming.
03

Calculate the Number of Correct Answers

Since only one of the listed answers is correct, note that there is 1 correct answer.
04

Calculate Total Possibilities

There are 5 possible choices in total. Represent this as the denominator in the probability fraction.
05

Set Up the Probability Expression

The probability of randomly picking the correct answer is given by the ratio of the number of correct answers to the total number of possibilities. Hence, the probability is \[\frac{1}{5}\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

random guessing
When faced with a multiple-choice question and you have no clue about the answer, you might resort to random guessing. This means you select an answer without any knowledge or strategy. In other words, each option has an equal chance of being chosen.
For example, in the given problem, you are guessing who discovered penicillin among five choices. Since you don't know the answer, your guess is purely random.
probability calculation
Probability calculation helps us quantify the likelihood of a certain event occurring. In the context of our problem, we calculate the probability of guessing the correct answer. This is done by dividing the number of correct answers by the total number of possible answers. The formula used here is:
\[ P(\text{correct answer}) = \frac{\text{Number of correct answers}}{\text{Total number of possibilities}} \]
By doing this, we figure out how likely it is to guess Alexander Fleming correctly out of the five choices.
correct answer identification
To pinpoint the correct answer, you first need to figure out which option answers the question accurately. Our problem states that Alexander Fleming discovered penicillin.
This identification step is crucial because it determines the numerator in our probability fraction. We have only one correct answer out of several possible options, which simplifies our calculation.
fraction representation
Fractions are a key part of expressing probability. A fraction consists of a numerator (top number) and a denominator (bottom number).
In our example, we set up the fraction with 1 as the numerator (since there's one correct answer) and 5 as the denominator (since there are 5 possible answers).
So, we state the probability of guessing Alexander Fleming correctly as:
\[ \frac{1}{5} \]
This means there is a 1 in 5 chance of guessing the right answer randomly.
total possibilities
Total possibilities refer to all the possible outcomes you can choose from in a scenario. In our problem, the total possibilities are the number of answer choices given in the question.
  • Sean Penn
  • William Penn
  • Penn Jillette
  • Alexander Fleming
  • Louis Pasteur

Thus, we have 5 total possibilities. These possibilities form the denominator in our probability fraction, resulting in:
\[ \frac{1}{5} \]

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