Answer:
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%
