On a 3 day vacation to Seattle the local weather forecaster predicts a 60% chance of rain everyday.What is the probability that it will rain everyday of the vacation.(round to the nearest thousandth)
Prob(rain 1stday)*prob(rain 2nd day)*prob(rain 3rd day)
= (.6)(.6)(.6) = .216
I do not believe you can apply statistics to weather in the manner described... Especially in Seattle, where rainy periods come in long cycles that are often incorrectly predicted. (I am from Seattle, and spend a month or two there every year). The weather you get one day is strongly correlated with that of previous days.
Reiny has given you the answer they are probably looking for, but I believe a more realistic value is more like 35%.
They picked a poor example for teaching purposes.
To find the probability that it will rain every day of the vacation when there is a 60% chance of rain each day, we can multiply the individual probabilities together.
In this case, the probability of rain on each day is 0.60 (or 60%).
Therefore, the probability of rain all three days is:
0.60 * 0.60 * 0.60 = 0.216
So, the probability that it will rain every day of the vacation is approximately 0.216 or 21.6% (rounded to the nearest thousandth).