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# There is an 80% chance David will eat a healthy breakfast an

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There is an 80% chance David will eat a healthy breakfast an [#permalink]  29 Nov 2019, 04:34
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Question Stats:

33% (01:13) correct 66% (00:51) wrong based on 6 sessions
There is an 80% chance David will eat a healthy breakfast and a 25% chance that it will rain. If these events are independent, what is the probability that David will eat a healthy breakfast OR that it will rain?

(A) 20%
(B) 80%
(C) 85%
(D) 95%
(E) 105%
[Reveal] Spoiler: OA
Senior Manager
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Kudos [?]: 51 [0], given: 137

Re: There is an 80% chance David will eat a healthy breakfast an [#permalink]  29 Nov 2019, 04:43
Need explanation
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Joined: 10 Apr 2015
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Re: There is an 80% chance David will eat a healthy breakfast an [#permalink]  29 Nov 2019, 06:39
2
KUDOS
Expert's post
huda wrote:
There is an 80% chance David will eat a healthy breakfast and a 25% chance that it will rain. If these events are independent, what is the probability that David will eat a healthy breakfast OR that it will rain?

(A) 20%
(B) 80%
(C) 85%
(D) 95%
(E) 105%

P(A or B) = P(A) + P(B) - P(A and B)
So, P(healthy breakfast OR rain) = P(healthy breakfast) + P(rain) - P(healthy breakfast AND rain)

Note: since P(healthy breakfast) and P(rain) are INDEPENDENT, P(healthy breakfast AND rain) = P(healthy breakfast) x P(rain)
= 0.8 x 0.25
= 0.2

So, P(healthy breakfast OR rain) = P(healthy breakfast) + P(rain) - P(healthy breakfast AND rain) = 0.8 + 0.25 - 0.2 = 0.85

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Joined: 22 Jun 2019
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Kudos [?]: 51 [0], given: 137

Re: There is an 80% chance David will eat a healthy breakfast an [#permalink]  29 Nov 2019, 06:46
GreenlightTestPrep wrote:
huda wrote:
There is an 80% chance David will eat a healthy breakfast and a 25% chance that it will rain. If these events are independent, what is the probability that David will eat a healthy breakfast OR that it will rain?

(A) 20%
(B) 80%
(C) 85%
(D) 95%
(E) 105%

P(A or B) = P(A) + P(B) - P(A and B)
So, P(healthy breakfast OR rain) = P(healthy breakfast) + P(rain) - P(healthy breakfast AND rain)

Note: since P(healthy breakfast) and P(rain) are INDEPENDENT, P(healthy breakfast AND rain) = P(healthy breakfast) x P(rain)
= 0.8 x 0.25
= 0.2

So, P(healthy breakfast OR rain) = P(healthy breakfast) + P(rain) - P(healthy breakfast AND rain) = 0.8 + 0.25 - 0.2 = 0.85

Cheers,
Brent

I have a little bit confusion here, before shed some light on my confusion i want to say that,i watched your video related this topic (mutually exclusive, dependent and independent events).

We use this formula when Both Events are mutually exclusive ---First One: P(A or B) = P(A) + P(B), and
When they are not mutually exclusive ----- Second One: P(A or B) = P(A) + P(B) - P(A and B)

NOw above question both event are there mutually exclusive so as rules we need to follow the 1st one but why we used the 2nd one?
GRE Instructor
Joined: 10 Apr 2015
Posts: 2608
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Kudos [?]: 2811 [2] , given: 45

Re: There is an 80% chance David will eat a healthy breakfast an [#permalink]  29 Nov 2019, 07:02
2
KUDOS
Expert's post
huda wrote:
GreenlightTestPrep wrote:
huda wrote:
There is an 80% chance David will eat a healthy breakfast and a 25% chance that it will rain. If these events are independent, what is the probability that David will eat a healthy breakfast OR that it will rain?

(A) 20%
(B) 80%
(C) 85%
(D) 95%
(E) 105%

I have a little bit confusion here, before shed some light on my confusion i want to say that,i watched your video related this topic (mutually exclusive, dependent and independent events).

We use this formula when Both Events are mutually exclusive ---First One: P(A or B) = P(A) + P(B), and
When they are not mutually exclusive ----- Second One: P(A or B) = P(A) + P(B) - P(A and B)

NOw above question both event are there mutually exclusive so as rules we need to follow the 1st one but why we used the 2nd one?

For all OR probability questions, we can always use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
However, when it turns out the two events are mutually exclusive, then P(A and B) = 0

In this particular question, we're told that the two events are independent, which means P(A and B) = P(A) x P(B) = (0.8) x (0.25) = 0.2
Since P(A and B) = 0.2 (i.e., P(A and B) does NOT equal zero), we can conclude that the two events are not mutually exclusive

Does that help?

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

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Posts: 379
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Kudos [?]: 51 [0], given: 137

Re: There is an 80% chance David will eat a healthy breakfast an [#permalink]  29 Nov 2019, 07:07
Re: There is an 80% chance David will eat a healthy breakfast an   [#permalink] 29 Nov 2019, 07:07
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