/*! 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 100 A slot machine has three slots; ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 100

A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. If each of the four items is equally likely to appear on a given spin, what is your probability of winning?

Short Answer

Expert verified
Answer: The probability of winning on the slot machine is 1/16 or approximately 0.0625, which is 6.25%.

Step by step solution

01

Find the total number of possible outcomes.

Since there are four items, and each slot can have one of these items, the total number of possible outcomes is 4 * 4 * 4, as each slot can have any of the four items independently of the other slots. Multiply the possibilities for each slot to get the total number of outcomes in the sample space. Total outcomes = 4 * 4 * 4 = 64
02

Find the number of winning outcomes.

A winning outcome occurs when all three slots show the same item. There are four items, and each item can lead to a winning outcome. Therefore, there are four possible winning outcomes. Winning outcomes = 4 (one for each item)
03

Calculate the probability of winning.

To find the probability of winning, we need to divide the number of winning outcomes by the total number of possible outcomes in the sample space. Probability of winning = (winning outcomes) / (total outcomes) Probability of winning = 4 / 64 Probability of winning = 1 / 16 So the probability of winning of the slot machine is 1/16 or approximately 0.0625, which is 6.25%.

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

Identify the following as discrete or continuous random variables: a. Total number of points scored in a football game b. Shelf life of a particular drug c. Height of the ocean's tide at a given location d. Length of a 2-year-old black bass e. Number of aircraft near-collisions in a year

A retailer sells two styles of highpriced digital video recorders (DVR) that experience indicates are in equal demand. (Fifty percent of all potential customers prefer style \(1,\) and \(50 \%\) favor style 2.) If the retailer stocks four of each, what is the probability that the first four customers seeking a DVR all purchase the same style?

A random variable \(x\) has this probability distribution: $$\begin{array}{l|rrrrrr}x & 0 & 1 & 2 & 3 & 4 & 5 \\\\\hline p(x) & .1 & .3 & .4 & .1 & ? & .05\end{array}$$ a. Find \(p(4)\). b. Construct a probability histogram to describe \(p(x)\). c. Find \(\mu, \sigma^{2},\) and \(\sigma\). d. Locate the interval \(\mu \pm 2 \sigma\) on the \(x\) -axis of the histogram. What is the probability that \(x\) will fall into this interval? e. If you were to select a very large number of values of \(x\) from the population, would most fall into the interval \(\mu \pm 2 \sigma ?\) Explain.

You have three groups of distinctly different items, four in the first group, seven in the second, and three in the third. If you select one item from each group, how many different triplets can you form?

An investor has the option of investing in three of five recommended stocks. Unknown to her, only two will show a substantial profit within the next 5 years. If she selects the three stocks at random (giving every combination of three stocks an equal chance of selection), what is the probability that she selects the two profitable stocks? What is the probability that she selects only one of the two profitable stocks?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.