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

Question

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%

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

AvidDreamer09 · Accepted Answer

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%

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

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

fskilnik · Answer

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  .

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

Regards, 
Fabio.

hudacse6 · Answer

any other solution?

TestPrepUnlimited · Answer

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

Fdambro294 · Answer

If 2 events are Independent of each other, then this implies that the 2 events are NOT Mutually exclusive (the events have a chance of happening at the same time)

P(Eat Healthy OR Rain) = P(eat healthy) + P(rain) - P(eat healthy AND rain)

If 2 events (event A and event B) are independent, the probability of (A and B) occurring is simply the product of the probabilities (whether one event occurs does not impact the probability that the other event occurs)

P(eat healthy AND rain) = (.8) * (.25) = .2
 
(Because 1/4th of .8 is —— > .2)

= (.8) + (.25) - (.2)

= .85

85%

Posted from my mobile device

qadro · Answer

one of the answers that says reverse the ask is not intuitive. at the same time some folks above suggest P(A&B) is P(A)*P(B). At first glance the latter may not appear to be true, but it is . here is how:

P(A&B) = P(a|b). P(b)

given that events are independent, then P(a|b)=P(a). hence the acceptable use of product. rest you can figure out.

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

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