13 x 17n - 13 x 15
= 221n - 195
Using the hypergeometric distribution, it is found that there is a 0.0455 = 4.55% probability that both light bulbs failed the test.
The bulbs are chosen without replacement, and this is why the <u>hypergeometric distribution</u> is used to find the probability.
Hypergeometric distribution:
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- 12 bulbs, thus
- 3 failed the test, thus .
- 2 are selected, thus .
The probability that <u>both failed the test</u> is P(X = 2), thus:
0.0455 = 4.55% probability that both light bulbs failed the test.
A similar problem is given at brainly.com/question/24826394
Let's define variables:
x: number of times the ticket price increases ($ 1).
The income is given by:
I(x) = (15 + x)(500-20x)
We can rewrite this function in the following way:
I (x) = - 20x ^ 2 + 200x + 7500
We use the following equation to find the maximum:
max = (-b)/(2a)
where:
then, we have:
max = (-200)/(2(-20))
max = (200)/(40)
max=5
Thus, the ticket price that maximizes the benefit is:
15 + x = 15 + 5 = 20 $
Answer:
A ticket price that will maximize the charity's profit, if there are total 500 seats in the concert hall is:
$ 20
The part you don't need is "there are 10 periods in all during a week" because once you read the first two sentences you can tell you just need to do 24 x 2 which equals 48.
*Hope i helped :D