GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2019, 16:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # P(A) and P(B) are the probabilities of independent events A and B, re

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7740
GMAT 1: 760 Q51 V42 GPA: 3.82
P(A) and P(B) are the probabilities of independent events A and B, re  [#permalink]

### Show Tags

1
5 00:00

Difficulty:   25% (medium)

Question Stats: 69% (01:00) correct 31% (01:03) wrong based on 143 sessions

### HideShow timer Statistics

[GMAT math practice question]

P(A) and P(B) are the probabilities of independent events A and B, respectively. What is P(A)∙P(B)?

1) The probability that event A occurs but event B does not occur is 0.35.
2) The probability that event A occurs is 0.5.

_________________
Retired Moderator D
Joined: 25 Feb 2013
Posts: 1193
Location: India
GPA: 3.82
P(A) and P(B) are the probabilities of independent events A and B, re  [#permalink]

### Show Tags

1
MathRevolution wrote:
[GMAT math practice question]

P(A) and P(B) are the probabilities of independent events A and B, respectively. What is P(A)∙P(B)?

1) The probability that event A occurs but event B does not occur is 0.35.
2) The probability that event A occurs is 0.5.

for independent events -

P(A∩B)=P(A).P(B)

Statement 1: implies - P(only A)=0.35

but nothing mentioned about P(B). Insufficient

Statement 2: P(A)=0.5, but we don't know the value of P(B). Insufficient

Combining 1 & 2. we get P(only A) and P(A). so in a Venn diagram the common area between P(A) and P(B) i.e P(A∩B) = P(A)-P(only A)

or P(A).P(B)=P(A∩B)=0.5-0.35=0.15. Sufficient

Option C

Originally posted by niks18 on 09 Nov 2017, 02:28.
Last edited by niks18 on 13 Nov 2017, 12:53, edited 1 time in total.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7740
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: P(A) and P(B) are the probabilities of independent events A and B, re  [#permalink]

### Show Tags

=>
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

Since we have 2 variables P(A) and P(B), and no equation, C is most likely to be the answer.

Since events A and B are independent, P(A∩B) = P(A) ∙P(B) and P(B) = P(A∩B) / P(A).

Condition 1) & 2)
Since P(only A) = 0.35 and P(A) = 0.5, we have P(A) ∙P(B) = P(A∩B) = 0.15.
Both conditions 1) and 2) together are sufficient.

Therefore, the answer is C as expected.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.
Answer: C
_________________
Manager  G
Joined: 21 Jun 2017
Posts: 227
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: P(A) and P(B) are the probabilities of independent events A and B, re  [#permalink]

### Show Tags

1. 0.35 = P(A).(1-P(B))
2. P(A)

C Suff
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!! Re: P(A) and P(B) are the probabilities of independent events A and B, re   [#permalink] 04 Oct 2018, 09:31
Display posts from previous: Sort by

# P(A) and P(B) are the probabilities of independent events A and B, re

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  