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

P(Healthy Breakfast) = 4/5 P(NOT Healthy Breakfast) = 1/5
P(Rain) = 1/4 P(NOT Rain) = 3/4

P(David will eat a healthy breakfast OR that it will rain) = P(Healthy Breakfast and NOT Rain) + P(NOT Healthy Breakfast and it Rains) + P(Healthy Breakfast and it Rains)

= (4/5 x 3/4) + (1/5 x 1/4) + (4/5 x 1/4)
= 12/20 + 1/20 + 4/20
= 17/20
= 85/100

Hence, Option C (85%)

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