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Manager  Joined: 10 Feb 2011
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What is the probability that event E or event F or both will  [#permalink]

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2
16 00:00

Difficulty:   45% (medium)

Question Stats: 51% (00:46) correct 49% (00:49) wrong based on 382 sessions

### HideShow timer Statistics What is the probability that event E or event F or both will occur?

(1) The probability that event E will occur is 0.6.
(2) The probability that event F will occur is 0.4.
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
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Re: : What is the probability that event E or event F or both w  [#permalink]

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1
1
Yeah it hit me. P(E) + P(F) =1.0 This means the overlap is unknown. P(E and F) has to be known to solve this scenario. Hence E
Manager  Joined: 14 Feb 2011
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Re: : What is the probability that event E or event F or both w  [#permalink]

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2
We do not know whether events E & F are independent events, so can't conclude anything from given information in either 1) or 2), Hence E
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Re: : What is the probability that event E or event F or both w  [#permalink]

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The Ans will be E as it is not specified that the events are mutually exclusive.

If the events are mutually exclusive then the prob = 0

However, if there is an overlap, then we'd need the prob of e & f happening together to calculate the ans.
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Re: : What is the probability that event E or event F or both w  [#permalink]

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dreambeliever wrote:
If the events are mutually exclusive then the prob = 0

I mean ans = 1 in case of mutually exclusive.
Intern  Joined: 03 Mar 2010
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Re: : What is the probability that event E or event F or both w  [#permalink]

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2
1
If we agree that
1. (E OR F) means E, or F, or both will occur
2. (E AND F) means both will occur

then we have (see MGMAT Guide 4 page 87)

P(E OR F) = P(E) + P(F) - P(E AND F)

Here P(E AND F) is not given, so the answer is E.
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Manager  Joined: 05 Jan 2011
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Re: : What is the probability that event E or event F or both w  [#permalink]

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bogos wrote:
If we agree that
1. (E OR F) means E, or F, or both will occur
2. (E AND F) means both will occur

then we have (see MGMAT Guide 4 page 87)

P(E OR F) = P(E) + P(F) - P(E AND F)

Here P(E AND F) is not given, so the answer is E.

P(E OR F) = P(E) + P(F) - P(E AND F) is true if E and F are dependent events.However if they are independent Events P(E OR F) = P(E) + P(F) .Question does not provide information ..whether E and F are dependent/ independent event ...so it should be E
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Re: : What is the probability that event E or event F or both w  [#permalink]

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The formula is always true. MGMAT just clarifies the point by seperating the two cases.
In fact, we have:
P(E AND F) = 0 if E and F are independent.
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Re: : What is the probability that event E or event F or both w  [#permalink]

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1
Quote:
P(E AND F) = 0 if E and F are independent.

Not true, P(E AND F) = 0 if E and F are MUTUALLY EXCLUSIVE.

To say that E and F are independent means only that the outcome of E has no effect on the outcome of F and vice versa.

Quote:
P(E OR F) = P(E) + P(F) - P(E AND F) is true if E and F are dependent events.However if they are independent Events P(E OR F) = P(E) + P(F)

If they are independent events you still need the -P(E and F)

For example:
If you flip two coins (coins 1 and 2) at the same time, and we call the event that coin 1 lands heads "E" and the event the coin 2 lands heads "F", what is P(E or F)?

P(E) = .5
P(F) = .5
P(E or F) does not equal 1.
Manager  Joined: 31 Oct 2011
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Independent probability

Ifor example, if two coins are flipped the chance of both being heads is 

Mutually exclusive
If either event A or event B or both events occur on a single performance of an experiment this is called the union of the events A and B denoted as .

For example, the chance of rolling a 1 or 2 on a six-sided die is

This is from Wikipedia. I found this when I was searching for the explanation for this question.
But I am still confused the difference between independent probability and mutually exclusive.
To me, they sound the same. Help me understand them.
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Re: What is the probability that event E or event F or both will  [#permalink]

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eybrj2 wrote:
What is the probability that event E or event F or both will occur?

(1) The probability that event E will occur is 0.6
(2) The probability that event F will occur is 0.4

What is asked is the value of P(E)+P(F)+P(E union F)
we cannot determine (E union F) combining 1 & 2 as well. Hence the answer is E
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Manager  Joined: 13 May 2010
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Re: What is the probability that event E or event F or both will  [#permalink]

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shouldn't this be P(e) + P(f) and so the answer C Why E?
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Re: What is the probability that event E or event F or both will  [#permalink]

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Hi Bunuel,

I am not clear why E is the answer...

we have to find P(E)+P(F) + P(EUF), so using Stm1 and Stm 2, we should be able to find.

i.e 0.6 +0.4 + ( 0.6x0.4)...

So, Isn't the answer should be C

Thanks
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Re: What is the probability that event E or event F or both will  [#permalink]

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Mountain14 wrote:
Hi Bunuel,

I am not clear why E is the answer...

we have to find P(E)+P(F) + P(EUF), so using Stm1 and Stm 2, we should be able to find.

i.e 0.6 +0.4 + ( 0.6x0.4)...

So, Isn't the answer should be C

Thanks

I'm not Bunuel but I'm sure I can help

P (A and B) = P(A) * P (B/A). That means the probability of B given that A happens. Now only way that the second term is equal to P(B) is if they are independent events, otherwise the probability will be affected. For instance if you have some balls to pick from and you remove some and don't replace them then successive probabilities will change right? So back to the question, Are they independent events? We just don't know this.

Hope it helps brother
Cheers!
K PS. Just as a side note check also Mutually exclusive events in the GMAT Club Math Book just to be clear with those Probability concepts
Intern  Joined: 22 Jan 2014
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Re: What is the probability that event E or event F or both will  [#permalink]

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Hi we have no information weather E and F are independent events. So we cant answer the question even by considering the two choices
So ans should be E
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Re: What is the probability that event E or event F or both will  [#permalink]

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banksy wrote:
What is the probability that event E or event F or both will occur?

(1) The probability that event E will occur is 0.6.
(2) The probability that event F will occur is 0.4.

we are asked P(E or F) + P(E and B)
usually, if the two events are mutually exclusive, then:
P(E) + P(F)=1. - and P(E or F)=1, and P(E and F)=0.
if not, then:
P(E or F) = P(E) + P(F) + P(E and F)
and P(E or F)+P(E and F) = P(E) + P(F)

moreover, it might be conditional probability...

1. P(E)=0.6, but we do not know anything about P(F), or about what kind of events these two are. Moreover, we do not know whether there are any relations between these two. not sufficient.

2. P(F)=0.4 - same as 1. so no

at this moment, we crossed A, B, and D. our chances of getting to the right answer increased considerably - probability 50% (see how I used probability even here? :D)

ok, so it might appear that the two events are independent, since P(E)+P(F)=1.
but what if we have a conditional probability?
what if F can be chosen only if E is chosen?

in this case, the probability of getting F is P(E)* # of successes/total outcomes left = 4/10
since we do not know the relationship between these two events, then we cannot give a definite answer.

E
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GMAT 1: 750 Q49 V43 What is the probability that event E or event F or both will  [#permalink]

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banksy wrote:
What is the probability that event E or event F or both will occur?

(1) The probability that event E will occur is 0.6.
(2) The probability that event F will occur is 0.4.

REMEMBER TWO TERMS:-
1) Mutually exclusive events (rolling and dice AND tossing a coin) INDEPENDENT of each other
2) Mutually non exclusive events (Rolling a Dice and getting a number less than 6 OR a prime number ; 2,3, 5 are less than 6 as well as prime)

For two events Probability is defined in terms of Probability of First event ,Probability of second event ,Probability of both events and Probability of none of the events.
P(E) + P(F) + P(E & F) + P(None) = 1

If the events are mutually exclusive, meaning that both events cannot happen together - than Probability of P(E and F) will be 0.
But if events are not mutually exclusive then we must know the probability of none to calculate probability of both happening together
Since neither the stimulus nor any of the options gives us P(None) , we cannot find the probability

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Re: What is the probability that event E or event F or both will  [#permalink]

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Hii

Even if P(E) +P(F) had been 0.8 or 1.2, overlap would be unknown.
Rightly stated by you, it is E

gmat1220 wrote:
Yeah it hit me. P(E) + P(F) =1.0 This means the overlap is unknown. P(E and F) has to be known to solve this scenario. Hence E

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Re: What is the probability that event E or event F or both will  [#permalink]

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