/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 28 Find the probability and answer ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 28

Find the probability and answer the questions. On their first date, Kelly asks Mike to guess the date of her birth, not including the year. a. What is the probability that Mike will guess correctly? (Ignore leap years.) b. Would it be unlikely for him to guess correctly on his first try?

Short Answer

Expert verified
a. \[ \frac{1}{365} \]; b. It is highly unlikely.

Step by step solution

01

Identify Total Possible Outcomes

Since we are ignoring leap years, there are 365 possible days in a year. Therefore, the total number of possible outcomes is 365.
02

Identify Favorable Outcomes

The number of favorable outcomes is 1 because there is only one correct birth date.
03

Calculate Probability

The probability of guessing correctly is the ratio of the number of favorable outcomes to the total number of possible outcomes. Thus, the probability is given by: \[ P(\text{correct guess}) = \frac{1}{365}. \]
04

Assess Likelihood

To determine if it would be unlikely for Mike to guess correctly, we can compare the probability calculated. Since \[ \frac{1}{365} \] is a very small value, it indicates that it is highly unlikely for Mike to guess correctly on his first try.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

probability
Probability is a measure used to quantify the likelihood of a certain event happening. It ranges from 0 to 1, where 0 means the event will not happen and 1 means the event will certainly happen. In our problem, we are trying to find the probability of Mike guessing Kelly's birth date correctly. The formula for probability is: \( P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \). This formula helps us understand how likely an event is to occur, given the number of outcomes that count as 'favorable' and the total number of different possible outcomes.
favorable outcomes
Favorable outcomes are the specific outcomes of an event that we are interested in. In the context of our problem, the favorable outcome is Mike correctly guessing Kelly's birth date. Since there is only one correct birth date for Kelly, the number of favorable outcomes is 1. Understanding favorable outcomes helps in determining the probability by focusing on the outcomes that meet the criteria we are interested in.
total possible outcomes
The total number of possible outcomes is a key part of any probability calculation. It represents all the outcomes that can occur in an event. In our example, since we are ignoring leap years, there are 365 possible days in a year. Hence, the total number of possible outcomes Mike can choose from is 365. This value serves as the denominator in our probability formula, providing a full scope of all potential outcomes for the given event.
likelihood assessment
Likelihood assessment helps us understand how probable or improbable a certain event is. After calculating the probability, we can assess whether the event is likely to occur or not. In our problem, the probability of Mike guessing correctly is \( \frac{1}{365} \) which is approximately 0.0027. This is a very small value, indicating that it is highly unlikely for Mike to guess Kelly's birth date correctly on his first try. This assessment can be useful in decision-making processes where understanding the likelihood of outcomes can influence choices.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Express all probabilities as fractions. A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

Express the indicated degree of likelihood as a probability value between 0 and \(1 .\) When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero.

Answer the given questions that involve odds. A roulette wheel has 38 slots. One slot is 0 , another is 00 , and the others are numbered 1 through 36 , respectively. You place a bet that the outcome is an odd number. a. What is your probability of winning? b. What are the actual odds against winning? c. When you bet that the outcome is an odd number, the payoff odds are \(1: 1\). How much profit do you make if you bet \(\$ 18\) and win? d. How much profit would you make on the \(\$ 18\) bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? (Recommendation: Don't actually try to convince any casino of this; their sense of humor is remarkably absent when it comes to things of this sort.)

Express all probabilities as fractions. In a horse race, a quinela bet is won if you selected the two horses that finish first and second, and they can be selected in any order. The 140 th running of the Kentucky Derby had a field of 19 horses. What is the probability of winning a quinela bet if random horse selections are made?

Describe the simulation procedure. (For example, to simulate 10 births, use a random number generator to generate 10 integers between 0 and 1 inclusive, and consider 0 to be a male and 1 to be a female.) Ten percent of people are left-handed. In a study of dexterity, 15 people are randomly selected. Describe a procedure for using software or a TI-83/84 Plus calculator to simulate the random selection of 15 people. Each of the 15 outcomes should be an indication of one of two results: (1) Subject is left- handed; (2) subject is not left-handed.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.