In a shipment of 20 packages, 7 packages were damaged. The packages are randomly inspected, one at a time, with replacement between each selection, until the fourth damaged package is discovered. Calculate the probability that exactly 12 packages are inspected.

11.9%

Step-by-step explanation:

 To find the solution, we will do it through combinations.

Which has the following formula:

nCx = n! / [x! * (n-x)!]

Now, to know the probability in the first 11 packages we have to calculate the probability of favorable results divided by the probability of the number of possible results.

Favorable cases:

First, the number of combinations in which 3 damaged packages can be chosen from 7 damaged packages:

7C3 = 7! / [3! * (7-3)!] = 35

Second, the number of combinations in which you can choose 8 good packages from 13 good ones:

13C8 = 13! / [8! * (13-8)!] = 1287

Possible results: Number of combinations in which 11 packages can be taken from the 20 available packages:

20C11 = 20! / [eleven! * (20-11)!] = 167960

Therefore, the probability for the first 11 packages is:

(35 * 1287) / 167960 = 0.2681

For the last package, for package 12 to be damaged it is also 7 - 3 = 4, from 20 - 11 = 9.

That is 4/9, it would be the probability.

Finally, the probability would be the multiplication of the first 11 by the number 12, like this:

0.2681 * 4/9 = 0.119

That is to say that the answer is 11.9%

18.75 gallons

step-by-step explanation:

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: