23 percent of all homes purchased were investments 800 homes were sold what is probability 175 of homes were for investment
0.7752
To calculate the probability that 175 out of 800 homes were purchased as investments, we need to use the binomial probability formula.
The binomial probability formula is:
P(x) = C(n, x) * p^x * (1-p)^(n-x)
Where:
P(x) is the probability of getting exactly x successes
n is the total number of trials
x is the number of successful trials
p is the probability of success on a single trial
(1-p) is the probability of failure on a single trial
C(n, x) is the number of combinations of n things taken x at a time
In this case:
n = 800 (the total number of homes)
x = 175 (the number of homes purchased as investments)
p = 0.23 (the probability of a home being purchased as an investment)
Using the formula, the probability that exactly 175 out of 800 homes were purchased as investments is:
P(175) = C(800, 175) * 0.23^175 * (1-0.23)^(800-175)
To calculate this, we need to evaluate the following expressions:
C(800, 175) ≈ 1.74975 * 10^244 (using a calculator or software)
0.23^175 ≈ 4.13204 * 10^(-144) (using a calculator or software)
(1-0.23)^(800-175) ≈ 0.00001 (using a calculator or software)
Now, we can calculate the final probability:
P(175) ≈ (1.74975 * 10^244) * (4.13204 * 10^(-144)) * 0.00001
The resulting probability is an extremely small number close to zero, indicating that the probability of exactly 175 out of 800 homes being purchased as investments is very unlikely.
To calculate the probability that a certain number of homes out of 800 were purchased as investments, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of exactly k successes (in this case, homes purchased as investments),
- n is the total number of trials (homes sold, which is 800),
- p is the probability of success on any given trial (the percentage of homes purchased as investments, which is 23% or 0.23),
- C(n, k) is the binomial coefficient, also known as "n choose k" and represents the number of combinations of n items taken k at a time.
Now, let's plug the values into the formula:
P(X = 175) = C(800, 175) * (0.23)^175 * (1 - 0.23)^(800 - 175)
To calculate the binomial coefficient C(800, 175), we can use a combination calculator or formula such as:
C(n, k) = n! / (k! * (n - k)!)
Now, let's calculate the probability step by step:
Step 1: Calculate the binomial coefficient:
C(800, 175) = 800! / (175! * (800 - 175)!)
Step 2: Calculate the probability:
P(X = 175) = C(800, 175) * (0.23)^175 * (1 - 0.23)^(800 - 175)
By performing the necessary calculations, you can find the probability that 175 out of 800 homes were purchased as investments.