### Binomial Experiment Probability CalculationIn this exercise, we will explore how to determine the probability of a certain number of successes in a binomial experiment. Here is the problem setup and instructions for Part 1 of the exercise.#### Problem SetupA binomial experiment is defined by:- The number of trials, $n$.- The probability of success in each trial, $p$.Given the parameters:- $n = 10$ (number of trials)- $p = 0.2$ (success probability for each trial)#### Instructions**Part 1 of 3:**(a) **Determine the Probability $P(2)$:** Calculate the probability of exactly 2 successes in 10 trials and round your answer to at least three decimal places.\[ P(2) = \]**Note:** No graphs or diagrams are provided in this part of the question. Simply input the calculated probability value.Use the following binomial probability formula for calculation:\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]Where:- $ \binom{n}{k} $ is the binomial coefficient.- $ k $ is the number of successes.**Example Calculation:**For $ n = 10 $, $ p = 0.2 $, and $ k = 2 $:\[ P(2) = \binom{10}{2} (0.2)^2 (0.8)^8 \]Ensure your answer reflects a rounded value to at least three decimal places before inputting it into the provided box.

n = 10 p = 0.2 q = 1- p = 1- 0.2 = 0.8

Answered: (a) Determine the probability P (2).

Math

Statistics

(a) Determine the probability P (2).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Olivia is contemplating buying a laser printer. The probability that she will buy a printer…

A: Given data is : Probability that she she will buy a printer manufactured by Epson PE=0.21…

Q: (c) Find the probability that all four tires have low air pressure. The probability that all four…

A: Here given probability distribution of X X = no of tire with low air pressure

Q: Given X and Y are independent events respectively. P (X) = 0.65, P (Y) = 0.15. Event Z refers to the…

A: Dear students as per guidelines we solve only first three subparts only.

Q: Find the probability of the indicated events if P(E)=0.3 , P(F)=0.4 , and P(F|E)=0.3 (a) P(E∩F)…

A: GivenP(E)=0.3P(F)=0.4P(F|E)=0.3

Q: (3) P(A| B) > 0, i.e., the conditional probability is always non-negative.

Q: Let E be the event that a new car requires engine work under warranty and let T be the event that…

A: Probability of car requires engine work under warranty =P(E)=0.05 Probability of car requires…

Q: Calculate the probability P(E). There are 32 students in categories and B combined. Some students…

Q: We have events A and B with P(A) = 0.4 and P(B) = 0.5. Given that P(B|A) = 0.3, find the probability…

Q: Twenty-three percent of U.S. employees who are late for work blame oversleeping. You randomly select…

A: According to the given information in this questionWe need to find the meanOf the binomial…

Q: Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children…

A: Let X be the random variable having probability mass function then we will find the expected value…

Q: Let A, B be independent events with P (A) = P (B) = 1/3. Find the probability that exactly one of…

A: Probability value is calculated by dividing the number of possible observations involve in the event…

Q: Let A and B be two events with probabilities P(A) = 0.6, P(B) = 0.4 and P(A and B) = 0.2. (a) Find…

A: Given: P(A) = 0.6 P(B) = 0.4 P(A and B) = 0.2 Plug in all the given values in the above formula.

Q: Find P(U or V)P(U or V).

A: Concept: Two events are said to be mutually exclusive if both the events cannot occur at the same…

Q: Consider events and with 'P(A) = 0.2 P(B) = 0.5 and P(AN B) = 0.1. Calculate the conditional A B…

A: We want to find value of p(A/B)

Q: We are asked to find the probability of event A occurring given that event B occurs. This is…

A: By conditional probability theorem, the probability of event A occurs, provided that the event B has…

Q: P(H ∩ B)=.375 P(H ∩ R)=.125 P(T ∩ B)=.375 P(T ∩ R)=.125 Using the same premise as the previous…

Q: Suppose events A and B are independent and P(A) = = 1 P(B) = 4 Find the probability. (Enter the…

Q: The probability of owning a cat is P(C) = 0.24, while the probability of owning a dog is P(D) =…

A: Given information P(C) = 0.24 P (D) = 0.52

Q: Translate the following statements using probability notation. Use X as the random variable. The…

A: Translate the statements using probability notation.

Q: Let A and B be two events such that P (A) = 0.46 and P (B) = 0.07 (a) Determine P (A ∪ B), given…

A: Given: A and B be two events such that P (A) = 0.46 P (B) = 0.07

Q: Find P(A|B) if A is a subset of B.

A: The formula of the conditional probability is, Subset of the event means the every outcomes of…

Q: A report announced that the median sales price of new houses sold one year was $231,000,and the…

Question

### Binomial Experiment Probability Calculation

In this exercise, we will explore how to determine the probability of a certain number of successes in a binomial experiment. Here is the problem setup and instructions for Part 1 of the exercise.

#### Problem Setup
A binomial experiment is defined by:
- The number of trials, $n$.
- The probability of success in each trial, $p$.

Given the parameters:
- $n = 10$ (number of trials)
- $p = 0.2$ (success probability for each trial)

#### Instructions
**Part 1 of 3:**

(a) **Determine the Probability $P(2)$:**
Calculate the probability of exactly 2 successes in 10 trials and round your answer to at least three decimal places.

\[ P(2) = \]

**Note:**
No graphs or diagrams are provided in this part of the question. Simply input the calculated probability value.

Use the following binomial probability formula for calculation:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

Where:
- $ \binom{n}{k} $ is the binomial coefficient.
- $ k $ is the number of successes.

**Example Calculation:**
For $ n = 10 $, $ p = 0.2 $, and $ k = 2 $:

\[ P(2) = \binom{10}{2} (0.2)^2 (0.8)^8 \]

Ensure your answer reflects a rounded value to at least three decimal places before inputting it into the provided box.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

### Binomial Experiment Analysis

**Context**:
A binomial experiment is conducted with a given number of trials $ n $ and a given success probability $ p $.

Given data:
- Number of trials, $ n = 10 $
- Success probability, $ p = 0.2 $

#### Part 1 of 3
**(a) Determine the Probability $ P(2) $**

Calculate the probability of exactly 2 successes in 10 trials. The answer should be rounded to at least three decimal places.
\[ P(2) = \boxed{0.302} \]

#### Part 2 of 3
**(b) Find the Mean**

Calculate the mean number of successes and round the answer to two decimal places.

Incorrect Example:
\[ \text{The mean is} \ \boxed{0.2}. \]

Correct Answer:
\[ \text{The mean is} \ \boxed{2.00}. \]

#### Part 3 of 3
**(c) Find the Variance and Standard Deviation**

Calculate the variance and standard deviation of the number of successes. The variance should be rounded to two decimal places, and the standard deviation should be rounded to at least three decimal places.

- The variance is $ \boxed{1.6} $
- The standard deviation is $ \boxed{1.265} $

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Given P(A) = 0.031, find the probability of the complementary event. 0.969 0.992 0.946 None of these 0.113
5.Prove the following properties of probability: P(A) = 1-P(A). b. For any events A and B, P(AUB) = P(A) + P (B) – P(AB). -
If P (A) = 0.6, P (B) =0.5 and P (A U B) = 0.9, find the following probabilities: (a) P (ANB) (b) P (A/B)
Use the attached image to compute the following probabilities:• P(B|A)• P(B ∩ A)• P(B0|A)• P(B0 ∩ A)
You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent
Use the appropriate formula to answer the question: • Independent Probability: P(A and B) = P(A) x P(B) • Conditional Probability: P(A n B) = P(A) x P(B|A) • Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) True or False: Events A and B are independent? P(A) = 0.60 P(B) = 0.70 P(A and B) = 0.42 True False
The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. Complete parts (a) and (b) below. Business graduates Business None degree degree male 181823 612083 female 166501 867055 • Find the probability that a randomly selected student is male, given that the student received a business degree. The probability that a randomly selected student is male, given that the student received a business degree, is I (Round to three decimal places as needed.) • Find the probability that a randomly selected student received a business degree, given that the student is female. The probability that a randomly selected student received a business degree, given that the student is female, is (Round to three decimal places as needed.)