I hope this is the right place to post this question.
I'm currently studying the 'Math Review' section of the Official Guide for GMAT Reivew. Thing were going pretty fine till I reached the last paragraph of the 'Discrete Probability' section on page 120.
For those of you who have the book, I would greatly appreciate it if someone could give me insight into how did they reach the conclusions in this paragraph.
I'll retype the question for easier reference.
Consider an experiment with events A, B and C for which P(A)= 0.23, P(B)= 0.40 and P(C)= 0.85,
Also suppose that A and B are mutually exclusive and B and C are independent.
P(A or B)= P(A)+P(B) since mutually exclusive
= 0.23+0.40 = 0.63
P(B or C)= P(B)+P(C)-P(B)P(C) by independence
=0.40+0.85 = 0.91
Note that P(A or C) and P(A and C) cannot be determined using the information given [I assume that's because the question didn't state whether they're mutually exclusive or independent in relevance to each other]
But it can be determined that A and C are not mutually exclusive since P(A)+P(C)=1.08, which is greater than 1, and therefore cannot equal P(A or C); from this it follows that P(A and C)>= 0.08. [How did they reach this conclusion? where did the 0.08 come from?]
The rest of the paragraph is clear.
Thank you in advance for any help.
I'm currently studying the 'Math Review' section of the Official Guide for GMAT Reivew. Thing were going pretty fine till I reached the last paragraph of the 'Discrete Probability' section on page 120.
For those of you who have the book, I would greatly appreciate it if someone could give me insight into how did they reach the conclusions in this paragraph.
I'll retype the question for easier reference.
Consider an experiment with events A, B and C for which P(A)= 0.23, P(B)= 0.40 and P(C)= 0.85,
Also suppose that A and B are mutually exclusive and B and C are independent.
P(A or B)= P(A)+P(B) since mutually exclusive
= 0.23+0.40 = 0.63
P(B or C)= P(B)+P(C)-P(B)P(C) by independence
=0.40+0.85 = 0.91
Note that P(A or C) and P(A and C) cannot be determined using the information given [I assume that's because the question didn't state whether they're mutually exclusive or independent in relevance to each other]
But it can be determined that A and C are not mutually exclusive since P(A)+P(C)=1.08, which is greater than 1, and therefore cannot equal P(A or C); from this it follows that P(A and C)>= 0.08. [How did they reach this conclusion? where did the 0.08 come from?]
The rest of the paragraph is clear.
Thank you in advance for any help.
