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 29​-page document and​ destroyed, it is page 15. ​B: When a different page is randomly selected and ripped from the​ document, it is page 24.

Required:
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

Answer 1

Answer and Step-by-step explanation:

In probability, events are dependent when the probability of the first event ocurring influences the outcome of the second event.

a. For events A and B, after ripping one page, it is destroyed, so the total number of pages changed. Therefore, events A and B are dependent.

b. To find the probability of both events happening, first, determine the probabilities of each event:

P(A) = $\frac{1}{29}$

P(B) = $\frac{1}{28}$

P(A and B) = $\frac{1}{29}.\frac{1}{28}$

P(A and B) = $\frac{1}{812}$

Probability of A and B occur is 0.12% or $\frac{1}{812}$.