Bounce1987 wrote:
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is
the same in that period?
(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.
If the probability it rains on one day is p, then the probability it does not rain on one day is 1-p. The probability it does not rain on the first two days is thus (1 - p)*(1 - p). So using Statement 1, we know:
(1 - p)^2 = 36/100
Take the square root, and 1-p = 6/10, so p = 4/10. So Statement 1 is equivalent to Statement 2 - both tell us that the probability of rain on any day is 0.4. That means the probability it rains on all three days is 0.4*0.4*0.4, so we can answer the question. So the answer is D.
I'm assuming above that the probability of rain on one day is independent of the probability of rain on any other day. You can only use the multiplication rules I used above when that's true. That's something that almost certainly is not true in real life (if it rains one day, that probably makes rain more likely the next day, which means they're not independent), so any question like this really needs to tell you the events are independent, because it's not a natural thing to assume. If you don't know the events are independent, you can't solve this. Where is the question from?
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