What is the probability that event E or event F or both will

Question

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.

beyondgmatscore · Accepted Answer

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

gmat1220 · Answer

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

dreambeliever · Answer

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.

dreambeliever · Answer

I mean ans = 1 in case of mutually exclusive.

bogos · Answer

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.

Onell · Answer

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

bogos · Answer

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.

jko · Answer

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.

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.

eybrj2 · Answer

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.

narangvaibhav · Answer

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

teal · Answer

shouldn't this be P(e) + P(f) and so the answer C Why E?

HarveyS · Answer

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

jlgdr · Answer

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

learning4mfailures · Answer

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

mvictor · Answer

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

LogicGuru1 · Answer

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

ANSWER IS E

GMATBusters · Answer

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

Kushchokhani · Answer

Bunuel

IMO we may add the tags "Overlapping Sets" and "Statistics and Sets Problems" to this ques

bumpbot · Answer

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What is the probability that event E or event F or both will

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