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In a shipment of 20 packages, 7 packages are damaged. The packages are randomly inspected, one at a time, without replacement, u

horsena [70]

Answer:

$\large\boxed{\large\boxed{0.119}}$

Explanation:

You need to find the probability that exactly three of the first 11 inspected packages are damaged and the fourth is damaged too.

1. Start with the first 11 inspected packages:

a) The number of combinations in which 11 packages can be taken from the 20 available packages is given by the combinatory formula:

$C(m,n)=\dfrac{m!}{m!(m-n)!}$

$C(20,11)=\dfrac{20!}{11!\cdot(20-11)!}$

b) The number of combinations in which 3 damaged packages can be chossen from 7 damaged packages is:

$C(7,3)=\dfrac{7!}{3!\cdot(7-3)!}$

c) The number of cominations in which 8 good packages can be choosen from 13 good pacakes is:

$C(13,8)=\dfrac{13!}{8!\cdot(13-8)!}$

d) The number of cominations in which 3 damaged packages and 8 good packages are chosen in the first 11 selections is:

$C(7,3)\times C(13,8)$

e) The probability is the number of favorable outcomes divided by the number of possible outcomes, then that is:

$\dfrac{C(7,3)\times C(13,8)}{C(20,11)}$

Subsituting:

$\dfrac{\dfrac{7!}{3!\cdot(7-3)!}\times \dfrac{13!}{8!\cdot(13-8)!}}{\dfrac{20!}{11!\cdot(20-11)!}}$

$=\dfrac{\dfrac{7!}{3!\cdot 4!}\times \dfrac{13!}{8!\cdot 5!}}{\dfrac{20!}{11!\cdot 9!}}=0.26818885$

2. The 12th package

The probability 12th package is damaged too is 7 - 3 = 4, out of 20 - 11 = 9:

3. Finally

The probability that exactly 12 packages are inspected to find exactly 4 damaged packages is the product of the two calculated probabilities:

$0.26818885\times 4/9=0.119$

6 0

4 years ago

Find the surface area of the prism. Length: 5 width: 8 height: 12 in

frez [133]

Answer:

The only answer I have for this could be 392in²

7 0

3 years ago

What is the tires weight in pounds?

poizon [28]

Hey!

To solve this problem we must begin by writing out an equation.

Here's the equation I've created.

520 ÷ 453.592 = ?

Now we solve our created equation to get the answer.

520 ÷ 453.592 = 1.1464046985

That could be our final answer but sometimes you might want to round.

So, the tires weight in pounds is 1.1464046985 or 1.15.

Hope this helps!

- Lindsey Frazier ♥

5 0

3 years ago

The lengths of the sides of a square are multiplied by 3.5. How is the ratio of the areas related to the ratio of the side lengt

Yakvenalex [24]

Answer:

A The ratio of the areas is the square of the ratio of the side lengths.

Step-by-step explanation:

10 x 3.5 = 35 and would be the same size each

35 x 35 = 1225

Ratio of areas = 10x10 and 10x3.5 x 10 x 3.5 = 100 : 1225 = 4: 49

Therefore just from doing this we can find easily by referring back to ratio above shown.

D IS NOT TRUE This means the ratio of the areas (1225) is the square root of the ratio (sqrt1225=35) of the side lengths (35:35) is not true

sqrt 1225 is 35 and becomes a square root of the area

Where matching this to ratio of sides is not true as 35:35= 1:1 and the ratio to the sides are not the same as ratio of two areas. But when we square we get the answer right.

when we cross multiply (division) we find find the ratio of areas 100:1225 is NOT TRUE AND NOT SAME AS ratio 10:35

We therefore left with DIVIDING THE ratio SIDES AS SIMPLIFIED into the Areas ABOVE to show-

1225/49 = 25 same here we have the area same ratio as 

100/4 = 25 same 

10:35 = 3.5^2 + 3.5^2 =12.50 + 12.50 = 25

A IS TRUE. as when we square the ratio 1=3.5 and add them together 1=3.5^2 +3.5^2 we get answer = 25

3 0

3 years ago

The perimeter of the square kitchen floor measures 48 feet. What is the area of the kitchen floor

poizon [28]

48/4 = 12 for sides. Area is l x w so 12x12 = 144

4 0

3 years ago

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