/*! 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 438 If two dice are cast, what is th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 438

If two dice are cast, what is the probability the sum will be less than 5 ?

Short Answer

Expert verified
The probability that the sum of the numbers rolled on both dice will be less than 5 is \(\frac{1}{6}\).

Step by step solution

01

Find the total number of possible outcomes

When two dice are rolled, each die has 6 possible outcomes (1, 2, 3, 4, 5, or 6) and the other die also has 6 possible outcomes. So, the total number of possible outcomes is 6*6 which equals 36.
02

Find the number of outcomes where the sum is less than 5

We need to find the number of possible outcomes where the sum of the numbers rolled on both dice is less than 5. Let's write down the possible outcomes that meet this condition: 1. Die 1 shows 1, Die 2 shows 1 (sum = 2) 2. Die 1 shows 1, Die 2 shows 2 (sum = 3) 3. Die 1 shows 1, Die 2 shows 3 (sum = 4) 4. Die 1 shows 2, Die 2 shows 1 (sum = 3) 5. Die 1 shows 2, Die 2 shows 2 (sum = 4) 6. Die 1 shows 3, Die 2 shows 1 (sum = 4) There are 6 outcomes where the sum is less than 5.
03

Calculate the probability of the sum being less than 5

To find the probability, we will divide the number of outcomes where the sum is less than 5 by the total number of possible outcomes. Probability = (Number of outcomes where the sum is less than 5) / (Total number of possible outcomes) Probability = 6 / 36 Probability = 1 / 6 The probability that the sum of the numbers rolled on both dice will be less than 5 is \(\frac{1}{6}\).

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

From 20 tickets marked with the first 20 numerals, one is drawn at random: find the chance that it is a multiple of 3 or of 7 .

A deck of playing cards is thoroughly shuffled and a card is drawn from the deck. What is the probability that the card drawn is the ace of diamonds?

An urn contains 6 white, 4 black, and 2 red balls. In a single draw, find the probability of drawing: (a) a red ball; (b) a black ball; (c) either a white or a black ball. Assume all outcomes equally likely.

In a factory four machines produce the same product. Machine A produces \(10 \%\) of the output, machine B, \(20 \%\), machine C, \(30 \%\), and machine \(\mathrm{D}, 40 \% .\) The proportion of defective items produced by these follows: Machine A: .001; Machine B: .0005; Machine C: .005; Machine D: .002. An item selected at random is found to be defective. What is the probability that the item was produced by A? by B?- by C? by \(\mathrm{D} ?\)

Your company uses a pre-employment test to screen applicants for the job of repairman. The test is passed by \(60 \%\) of the applicants. Among those who pass the test \(80 \%\) complete training successfully. In an experiment, a random sample of applicants who do not pass the test is also employed. Training is successfully completed by only \(50 \%\) of this group. If no pre- employment test is used, what percentage of applicants would you expect to complete training successfully?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

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.