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For the given pair of events A and​ B, complete parts​ (a) and​ (b) below. ​A: When a page is randomly selected and ripped from a 2424​-page document and​ destroyed, it is page 2020. ​B: When a different page is randomly selected and ripped from the​ document, it is page 1616. a. Determine whether events A and B are independent or dependent.​ (If two events are technically dependent but can be treated as if they are independent according to the​ 5% guideline, consider them to be​ independent.) b. Find​ P(A and​ B), the probability that events A and B both occur. a. Choose the correct answer below.

Respuesta :

Answer:

The two events are dependent.

the probability that events A and B both occur is:

[tex]\frac{1}{2424}\times \frac{1}{2423}=1.7026052585\times 10^{-7}\ or\ 0.00000017[/tex]

Step-by-step explanation:

Consider the provided information.

Event A: When a page is randomly selected and ripped from a 2424​-page document and​ destroyed, it is page 2020.

Event B: When a different page is randomly selected and ripped from the​ document, it is page 1616.

Part(A)

The occurring of one event affects the probability of the other event.

Because if we ripped one page then the probability of ripping second page will going to change as the size of sample space will decrease.

For example: The document has 2424 page, that means size of sample space is 2424. If we ripped another page, the sample size will be 2423. That means event B is depending on event A.

Thus, the two events are dependent.

Part(B)

The probability that events A and B both occur.

If we select a page randomly from 2424-page document, the probability will be: 1/2424

Now we have 2423 pages left in the document as one page is destroyed.

The probability of selecting another page is: 1/2423.

Thus, the probability that events A and B both occur is:

[tex]\frac{1}{2424}\times \frac{1}{2423}=1.7026052585\times 10^{-7}\ or\ 0.00000017[/tex]

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