/*! 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 30 A bag of 100 tulip bulbs purchas... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 30

A bag of 100 tulip bulbs purchased from a nursery contains 40 red tulip bulbs, 35 yellow tulip bulbs, and 25 purple tulip bulbs. (a) What is the probability that a randomly selected tulip bulb is red? (b) What is the probability that a randomly selected tulip bulb is purple? (c) Interpret these two probabilities.

Short Answer

Expert verified
a) 0.4 b) 0.25 c) 40% chance for red, 25% chance for purple.

Step by step solution

01

Identify Total Number of Bulbs

Total number of tulip bulbs is given as 100.
02

Probability of Selecting a Red Tulip Bulb

The probability of selecting a red tulip bulb is the number of red tulip bulbs divided by the total number of bulbs. \(P(\text{Red}) = \frac{\text{Number of Red Bulbs}}{\text{Total Number of Bulbs}} = \frac{40}{100} = 0.4\)
03

Probability of Selecting a Purple Tulip Bulb

The probability of selecting a purple tulip bulb is the number of purple tulip bulbs divided by the total number of bulbs. \(P(\text{Purple}) = \frac{\text{Number of Purple Bulbs}}{\text{Total Number of Bulbs}} = \frac{25}{100} = 0.25\)
04

Interpretation of the Probabilities

The probability of 0.4 for red tulip bulbs means that there is a 40% chance that a randomly selected tulip bulb will be red. The probability of 0.25 for purple tulip bulbs means that there is a 25% chance that a randomly selected tulip bulb will be purple.

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 Calculation
In this section, we will discuss how to calculate the probability of an event. Probability measures how likely an event is to occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
In our exercise, the total number of tulip bulbs is 100. To find the probability of selecting a red tulip bulb, we divide the number of red bulbs (40) by the total number of bulbs (100).
\( P(\text{Red}) = \frac{40}{100} = 0.4 \)
This gives us a probability of 0.4 or 40%. Similarly, to find the probability of selecting a purple tulip bulb, we divide the number of purple bulbs (25) by the total number of bulbs:
\( P(\text{Purple}) = \frac{25}{100} = 0.25 \)
This gives us a probability of 0.25 or 25%.
Calculating probabilities helps us predict the likelihood of different outcomes and is a fundamental aspect in the field of statistics and probability.
Interpretation of Probabilities
Understanding what probabilities tell us is crucial. A probability of 0.4 for red tulip bulbs means that if we were to randomly select a tulip bulb from the bag many times, approximately 40% of the time we would pick a red bulb. This doesn't guarantee that exactly every 4 out of 10 picks will be red, but it gives us an idea of the likelihood over a large number of trials.
Similarly, a probability of 0.25 for purple tulip bulbs means that out of 100 selections, we would expect to pick a purple tulip bulb about 25 times.
These interpretations help us understand and predict the outcomes better.
When interpreting probabilities, it's also important to remember that probabilities range from 0 to 1, where 0 means the event will not happen, and 1 means the event will certainly happen.
Step-by-Step Solution
Breaking down problems into steps makes them easier to manage. Let's review the steps we followed in the exercise:
Step 1: Identify the total number of tulip bulbs, which was given as 100.
Step 2: Calculate the probability of selecting a red tulip bulb by dividing the number of red bulbs (40) by the total number (100), resulting in \( P(\text{Red}) = 0.4 \).
Step 3: Calculate the probability of selecting a purple tulip bulb similarly by dividing the number of purple bulbs (25) by the total number (100), giving us \( P(\text{Purple}) = 0.25 \).
Step 4: Interpret what these probabilities mean in a practical sense, understanding that 0.4 or 40% means out of many trials, we expect 40% to be red tulip bulbs.
Breaking any problem into smaller steps makes it simpler to understand and solve, which is especially useful in probability calculations.

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

Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000 shipped. The probability that the first chip randomly selected is defective is \(\frac{50}{10,000}=0.005 .\) Compute the probability that two randomly selected chips are defective under the assumption of independent events. Compare your results to part (a). Conclude that, when small samples are taken from large populations without replacement, the assumption of independence does not significantly affect the probability.

According to the National Vital Statistics Report, \(20.1 \%\) of all pregnancies result in weight gain in excess of 40 pounds (for singleton births). In addition, \(49.5 \%\) of all pregnancies result in the birth of a baby girl. Assuming gender and weight gain are independent, what is the probability a randomly selected pregnancy results in a girl and weight gain in excess of 40 pounds?

Suppose that a shipment of 120 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality- control engineer randomly selects 4 of the components and tests them. If 1 or more of the components is defective, the shipment is rejected. What is the probability that the shipment is rejected?

My wife has organized a monthly neighborhood party. Five people are involved in the group: Yolanda (my wife), Lorrie, Laura, Kim, and Anne Marie. They decide to randomly select the first and second home that will host the party. What is the probability that my wife hosts the first party and Lorrie hosts the second? Note: Once a home has hosted, it cannot host again until all other homes have hosted.

Fingerprints are now widely accepted as a form of identification. In fact, many computers today use fingerprint identification to link the owner to the computer. In \(1892,\) Sir Francis Galton explored the use of fingerprints to uniquely identify an individual. A fingerprint consists of ridgelines. Based on empirical evidence, Galton estimated the probability that a square consisting of six ridgelines that covered a fingerprint could be filled in accurately by an experienced fingerprint analyst as \(\frac{1}{2}\). (a) Assuming that a full fingerprint consists of 24 of these squares, what is the probability that all 24 squares could be filled in correctly, assuming that success or failure in filling in one square is independent of success or failure in filling in any other square within the region? (This value represents the probability that two individuals would share the same ridgeline features within the 24 -square region.) (b) Galton further estimated that the likelihood of determining the fingerprint type (e.g., arch, left loop, whorl, etc.) as \(\left(\frac{1}{2}\right)^{4}\) and the likelihood of the occurrence of the correct number of ridges entering and exiting each of the 24 regions as \(\left(\frac{1}{2}\right)^{8}\). Assuming that all three probabilities are independent, compute Galton's estimate of the probability that a particular fingerprint configuration would occur in nature (that is, the probability that a fingerprint match occurs by chance).
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.