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Chapter 4: Problem 15

Express the indicated degree of likelihood as a probability value between \(\boldsymbol{0}\) and \(\boldsymbol{I}\).Based on a Harris poll, if you randomly select a traveler, there is a \(43 \%\) chance that his or her luggage is black.

Short Answer

Expert verified
0.43

Step by step solution

01

Identify the Given Percentage

The problem states there is a 43% chance that a traveler's luggage is black. This percentage will serve as the basis for converting it into a probability.
02

Convert Percentage to Decimal

To convert the percentage to a decimal, divide the percentage by 100. So, \[ P(\text{black luggage}) = \frac{43}{100} \]
03

Simplify the Expression

Perform the division to get the probability value as a decimal. \[ P(\text{black luggage}) = 0.43 \]

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Key Concepts

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

Expressing Likelihood
When we talk about probability, we are expressing the likelihood that a particular event will occur. This usually involves measuring the chance of an event happening using a number between 0 and 1. A probability of 0 means the event cannot happen, while a probability of 1 means it will certainly happen.
For example, in the given exercise, you are asked to express the likelihood that a traveler鈥檚 luggage is black. In simpler terms, you are determining how likely it is, or what the chances are, that a traveler's luggage will be black. Expressing likelihood in this way helps understand how probable or improbable an event is.
Converting Percentages
A large part of probability calculation involves converting percentages to decimal format. This is because percentages are often used to describe probabilities. However, mathematical operations with percentages are easier when they are in decimal form.
Here鈥檚 how you can convert a percentage to a decimal:
  • Identify the percentage you want to convert. In our exercise, we have a 43% chance.
  • Divide the percentage by 100. In this case, it鈥檚 \( \frac{43}{100} \).

    • After performing the division, the percentage 43% is converted to 0.43 in decimal format. Now it鈥檚 much easier to use in further calculations as a probability value.
Simplifying Mathematical Expressions
Simplifying mathematical expressions is an essential skill when working with probabilities. This usually involves breaking down expressions into more manageable parts.
For instance, after converting 43% to decimal form, you may need to further simplify the expression if required. Luckily, in our case, 0.43 is already a simplified and easy-to-understand form. However, always remember: if additional simplification is needed, follow these steps:
  • Keep the expression as a fraction: Sometimes working with fractions is simpler than decimals, especially if you need to multiply or divide them.
  • Use basic arithmetic operations: Always perform the fundamental math operations step-by-step.

    • In conclusion, simplifying expressions makes it easier to work with and understand probabilities, setting a foundation for more complex calculations in the future.

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Most popular questions from this chapter

Express all probabilities as fractions. A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available. a. If the subjects are selected and treated one at a time in sequence, how many different sequential arrangements are possible if 14 people are selected from the 16 that are available? b. If 14 subjects are selected from the 16 that are available, and the 14 selected subjects are all treated at the same time, how many different treatment groups are possible? c. If 14 subjects are randomly selected and treated at the same time, what is the probability of selecting the 14 youngest subjects?

Genetics: Simulating Population Control A classical probability problem involves a king who wanted to increase the proportion of women by decreeing that after a mother gives birth to a son, she is prohibited from having any more children. The king reasons that some families will have just one boy, whereas other families will have a few girls and one boy, so the proportion of girls will be increased. Is his reasoning correct? Will the proportion of girls increase?

Use the given sample space or construct the required sample space to find the indicated probability..Exercise 33 lists the sample space for a couple having three children. After identifying the sample space for a couple having four children, find the probability of getting three girls and one boy (in any order).

Find the probability and answer the questions. MicroSort's YSORT gender selection technique is designed to increase the likelihood that a baby will be a boy. At one point before clinical trials of the YSORT gender selection technique were discontinued, 291 births consisted of 239 baby boys and 52 baby girls (based on data from the Genetics \& IVF Institute). Based on these results, what is the probability of a boy born to a couple using MicroSort's YSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a boy?

Express all probabilities as fractions. Mendel conducted some his famous experiments with peas that were either smooth yellow plants or wrinkly green plants. If four peas are randomly selected from a batch consisting of four smooth yellow plants and four wrinkly green plants, find the probability that the four selected peas are of the same type.
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