Mathematics, 12.08.2020 05:01 kaylamcph7844

Suppose that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects. a. How many different samples can be chosen?
b. How many samples will contain at least one defective board?
c. What is the probability that a randomly chosen sample of five contains at least one defective board?

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Answer from: EllaSue

(a) 658,008 different samples can be chosen.

(b) 222,111 samples will contain at least one defective board.

Step-by-step explanation:

We are given that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects.

(a) To find how many different samples can be chosen, we will use a combination formula here because the order of selecting a sample of 5 from the production run of 40 doesn't matter.

Here, n = total sample = 40 and r = selected sample = 5

So, the combination formula is; $^{n}C_r= \frac{n!}{r! \times (n-r)!}$

$^{40}C_5= \frac{40!}{5! \times (40-5)!}$

$^{40}C_5= \frac{40!}{5! \times 35!}$

$^{40}C_5$ = 658,008 ways

So, 658,008 different samples can be chosen.

(b) To find how many samples will contain at least one defective board, we will first find how many samples will contain no or 0 defective board.

For this also, we will use a combination where n = 40 - 3 = 37 non-defective computer board and a sample of r = 5 computer boards.

So, $^{n}C_r= \frac{n!}{r! \times (n-r)!}$

$^{37}C_5= \frac{37!}{5! \times (37-5)!}$

$^{37}C_5= \frac{37!}{5! \times 32!}$

$^{37}C_5$ = 435,897 ways

This means that 435,897 of the 658,008 samples will contain no defective board.

Now, the samples that will contain at least one defective board = Total samples - Samples that contain no defective board

= 658,008- 435, 897

= 222,111

Required Probability = $\frac{222,111}{658,008}$

= 0.34 or 34%

Answer from: Quest

-by-step explanation:

it would be c

Pls only fo the first one i will mark brainliest

Answer from: Quest

the argument of alfred t. mahan, henry cabot lodge, and albert j. beveridge was the economically and mass production the the americans could not consume themselves. this led expansion to sell to other foreign nations for profits.

step-by-step explanation:

this is my explanation

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