Thank you for visiting Two friends are shooting at a target with air rifles They each have one bullet remaining Based on their shooting thus far the probability of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The probability mass function (PMF) for the variable X, the number of bullets that hit the target, is:
P(X = 0) = 0.0625
P(X = 1) = 0.375
P(X = 2) = 0.5625
Explanation:
To find the probability mass function (PMF) for the variable X, the number of bullets that hit the target, we can use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success.
In this case, we have two independent trials, as there are two marksman shooting at the target. Each marksman has a probability of 0.75 of hitting the target with their final bullet. Therefore, the probability of hitting the target is 0.75 for each marksman.
The possible values of X, the number of bullets that hit the target, range from 0 to 2. We can calculate the PMF for each possible value of X using the binomial distribution formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability that X takes the value k
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success in a single trial
- n is the number of trials
- k is the number of successes
Using this formula, we can calculate the PMF for each possible value of X:
P(X = 0) = C(2, 0) * 0.75^0 * (1 - 0.75)^(2 - 0) = 0.0625
P(X = 1) = C(2, 1) * 0.75^1 * (1 - 0.75)^(2 - 1) = 0.375
P(X = 2) = C(2, 2) * 0.75^2 * (1 - 0.75)^(2 - 2) = 0.5625
Therefore, the correct probability mass function for the variable X is:
P(X = 0) = 0.0625
P(X = 1) = 0.375
P(X = 2) = 0.5625
Learn more about probability mass function for number of bullets hitting the target here:
https://brainly.com/question/32598122
#SPJ11
Thank you for reading the article Two friends are shooting at a target with air rifles They each have one bullet remaining Based on their shooting thus far the probability of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
