For the given pair of events A and B, complete parts (a) and (b) below. A: When
ID: 3360201 • Letter: F
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 23 23-page document and destroyed, it is page 9
B: When a different page is randomly selected and ripped from the document, it is page 22
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 independent because the occurrence of one does not affect the probability of the occurrence of the other.
B.The two events are dependent 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.
b. The probability that events A and B both occur is ------
(Round to four decimal places as needed.)
Explanation / Answer
The probability of each event occuring P(A) = P(B) = 1/23.
If any one of the events occur, the probability of the other occuring P(A|B) = P(B|A) = 1/22.
a. Since the values are different, the events are not independent.
The correct answer is:
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) = P(A|B) P(B) = P(B|A) P(A) = 1/23 * 1/22 = 0.0020.