Hi

I have a question about the following problem in the Probability Fundamentals second video.

Greg solved it the following way.

P(rain) = 0.4

P(no rain) = 0.6

P(no rain on two consecutive days) = 0.6*0.6 = 0.36

Whereas, I solved it the following way.

P(rain) = 0.4

P(rain on day one AND day two) = 0.4*0.4 = 0.16

P(no rain on two consecutive days) = 1- 0.16 = 0.84

What am I doing wrong here?

The question ask for Not-Rain,Not-Rain = 0.36

What you’re getting here can be [rain on day 1 and not rain on day 2] or[ not rain on day 1 and rain on day 2] or [Not Rain on day 1 and Not-Rain on day 2] = .24 +.24 + .36 = .84

yes, but that is really confusing. I still can’t understand why Greg’s approach works and mine doesn’t.

This is not correct. The negation of there being no rain on two consecutive days does not imply that it rained on both days. Rather, it tells you the probability of having not rained *at least once* in these two days.

(edit: fixed error)

aaahh…now it all makes sense

I love Gregmat+ <3

there is also a related problem in this post of mine.

Confused with these probability problems - GRE Quant Problem Solving - Greg Mat+ Community Forum