An apartment building has 15 apartments in it. The tenant association is having a hard time collecting the fees from the tenants with an 0.6 probability of a tenant paying their fees. What is the probability of tenant association collecting fees from 11 out of the tenants ?

this is binomial ... collect or not collect

15C11 * .6^11 * .4^4

An apartment building has 15 apartments in it. The tenant association is having a hard time collecting the fees from the tenants with an 0.6 probability of a tenant paying their fees. What is the probability of tenant association collecting fees from 11 out of the tenants ?

15C11 * .6^11 * .4^4 what would be the probability be???

To find the probability of the tenant association collecting fees from 11 out of the 15 tenants, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:
P(X = k) is the probability of getting exactly k successes
C(n, k) is the combination formula for choosing k items from a set of n items
p is the probability of success for each trial
(1 - p) is the probability of failure for each trial
n is the number of trials

In this case, since the probability of a tenant paying their fees is 0.6, we can substitute the values in the formula as follows:

P(X = 11) = C(15, 11) * (0.6)^11 * (1 - 0.6)^(15 - 11)

To calculate the combination formula, we use the formula:

C(n, k) = n! / (k! * (n - k)!)

Let's calculate the probability step by step:

First, let's calculate the combination formula:

C(15, 11) = 15! / (11! * (15 - 11)!)
= 15! / (11! * 4!)
= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)
= 1365

Now let's substitute the values into the binomial probability formula:

P(X = 11) = 1365 * (0.6)^11 * (1 - 0.6)^(15 - 11)
= 1365 * (0.6)^11 * (0.4)^4

Calculating further:

P(X = 11) = 1365 * 0.0060466176 * 0.0256
= 21.6976

Therefore, the probability of the tenant association collecting fees from 11 out of the 15 tenants is approximately 0.2169 or 21.69%.