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

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Manager
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What is the probability that event E or event F or both will [#permalink]  01 Mar 2011, 09:57
00:00

Difficulty:

35% (medium)

Question Stats:

55% (01:27) correct 45% (00:35) wrong based on 49 sessions
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.
[Reveal] Spoiler: OA
Director
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Re: : What is the probability that event E or event F or both w [#permalink]  01 Mar 2011, 10:06

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.
Director
Status: Matriculating
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Posts: 931
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Kudos [?]: 191 [0], given: 123

Re: : What is the probability that event E or event F or both w [#permalink]  01 Mar 2011, 10:19
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
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Re: : What is the probability that event E or event F or both w [#permalink]  01 Mar 2011, 10:21
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
Manager
Joined: 24 Nov 2010
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Re: : What is the probability that event E or event F or both w [#permalink]  01 Mar 2011, 10:33
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.
Manager
Joined: 24 Nov 2010
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Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
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Re: : What is the probability that event E or event F or both w [#permalink]  01 Mar 2011, 10:37
dreambeliever wrote:
If the events are mutually exclusive then the prob = 0

I mean ans = 1 in case of mutually exclusive.
Intern
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Re: : What is the probability that event E or event F or both w [#permalink]  18 Mar 2011, 04:29
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
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Re: : What is the probability that event E or event F or both w [#permalink]  18 Mar 2011, 06:05
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
Intern
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Re: : What is the probability that event E or event F or both w [#permalink]  18 Mar 2011, 08:00
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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Current Student
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Re: : What is the probability that event E or event F or both w [#permalink]  18 Mar 2011, 10:18
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.
Re: : What is the probability that event E or event F or both w   [#permalink] 18 Mar 2011, 10:18
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