Question

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 26​-page document and​ destroyed, it is page 2. ​B: When a different page is randomly selected and ripped from the​ document, it is page 21. 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. A. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other. B. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. C. The two events are independent because the​ 5% guideline indicates that they should be treated as independent. D. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.

Answer 1

Answer:

a. D. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.

b.  P(A and​ B) = 1 ÷ 676

Step-by-step explanation:

a. The events are said to be independent event if occurrence of one event does not affect the other event.

The event A and B are dependent to each other, Since occurrence of one event does not affect the other event. Also page is selected from the same book.

Thus, Option D is correct.

b. If the both event are independent then,

P(A and B) = P(A∩B) = P(A) × P(B)

⇒P(A∩B) = $\frac{1}{26} \times\frac{1}{26} = \frac{1}{676}= 0.0014$