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# There is an 80% chance David will eat a healthy breakfast and a 25% ch

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Math Expert
Joined: 02 Sep 2009
Posts: 59674
There is an 80% chance David will eat a healthy breakfast and a 25% ch  [#permalink]

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03 Jan 2019, 11:46
00:00

Difficulty:

75% (hard)

Question Stats:

45% (01:43) correct 55% (01:20) wrong based on 49 sessions

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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%

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There is an 80% chance David will eat a healthy breakfast and a 25% ch  [#permalink]

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04 Jan 2019, 10:14
1
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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?

For probability its generally helpful to write this:
For And you must Multiply...

Using the set formula. We would have to subtract Both the events happening as the question stem asks you the probability for one of the events happening.
Then this becomes easy

P(HB or R) = P(HB) + P(R) - P(HB and R)
= 0.8 + 0.25 - (0.8 x 0.25)
= 0.85
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Re: There is an 80% chance David will eat a healthy breakfast and a 25% ch  [#permalink]

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04 Jan 2019, 12:05
Quote:
For probability its generally helpful to write this:
For And you must Multiply...

P(A and B) = P(A) * P(B) if, and only if, events A and B are independent.

P(A or B) = P(A) + P(B) if, and only if, P(A and B)=0 [and when A and B are mutually exclusive, it is the case].

These comments are carefully defined, explained and applied in the GMATH method.

Regards,
Fabio.
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Re: There is an 80% chance David will eat a healthy breakfast and a 25% ch  [#permalink]

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29 Nov 2019, 05:31
any other solution?
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There is an 80% chance David will eat a healthy breakfast and a 25% ch  [#permalink]

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29 Nov 2019, 12:18
Bunuel 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%

hudacse6

We can reverse the statement first, what is the probability that David will not eat a healthy breakfast AND it will not rain? That is 20%* 75% = 1/5 * 75% = 15%. This is the probability that we don't get our desired outcome, the rest of the probability space is our desired outcome so the answer is 100% - 15% = 85%.

Ans: C
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There is an 80% chance David will eat a healthy breakfast and a 25% ch   [#permalink] 29 Nov 2019, 12:18
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