/*! 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 24 A coin is tossed and a die is ro... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 24

A coin is tossed and a die is rolled. Find the probability of getting a tail and a number less than 5 .

Short Answer

Expert verified
The probability of throwing a tail on the coin and a number less than 5 on the die is \( \frac{1}{3} \).

Step by step solution

01

Determine the Probability of Each Event

Firstly, we need to calculate the individual probability of each event happening. For the coin flip, as it has 2 equally possible outcomes (heads and tails), \( P(Tail) = \frac{1}{2} \). Regarding the roll of the die, there are 6 equally likely outcomes (1,2,3,4,5,6), and 4 of them are less than 5 (1,2,3,4). Therefore, \( P(Die < 5) = \frac{4}{6} = \frac{2}{3} \).
02

Apply the Multiplication Principle

As these two events are independent, to find the probability of both events occurring simultaneously we need to multiply the probability of each event. \( P(Tail \: and \: Die < 5) = P(Tail) \times P(Die < 5) \)
03

Perform Calculation

Substituting the probabilities identified into the formula above, the calculation we need to perform becomes \( P(Tail \: and \: Die < 5) = \frac{1}{2} \times \frac{2}{3} \)
04

Simplify

Simplify the above equation to find the final probability: \( P(Tail \: and \: Die < 5) = \frac{1}{3} \).

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!

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

The tables in Exercises 3-4 show claims and their probabilities for an insurance company. a. Calculate the expected value and describe what this means in practical terms. b. How much should the company charge as an average premium so that it breaks even on its claim costs? c. How much should the company charge to make a profit of \(\$ 50\) per policy? PROBABILITIES FOR MEDICAL INSURANCE CLAIMS $$ \begin{array}{|c|c|} \hline \begin{array}{c} \text { Amount of Claim (to the } \\ \text { nearest } \mathbf{\$ 2 0 , 0 0 0 )} \end{array} & \text { Probability } \\ \hline \$ 0 & 0.70 \\ \hline \$ 20,000 & 0.20 \\ \hline \$ 40,000 & 0.06 \\ \hline \$ 60,000 & 0.02 \\ \hline \$ 80,000 & 0.01 \\ \hline \$ 100,000 & 0.01 \\ \hline \end{array} $$

A 25 -year-old can purchase a one-year life insurance policy for \(\$ 10,000\) at a cost of \(\$ 100\). Past history indicates that the probability of a person dying at age 25 is \(0.002\). Determine the company's expected gain per policy.

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. In a group of five men and five women, the probability of randomly selecting a man is \(\frac{1}{2}\), so if I select two people from the group, the probability that both are men is \(\frac{1}{2} \cdot \frac{1}{2}\).

A car model comes in nine colors, with or without air conditioning, with or without a sun roof, with or without automatic transmission, and with or without antilock brakes. In how many ways can the car be ordered with regard to these options?

License plates in a particular state display two letters followed by three numbers, such as AT- 887 or BB-013. How many different license plates can be manufactured for this state?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Probability and 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.