In a tropical location

Question

In a tropical location, there is a 68% chance of rain each day. What is the probability that a 3-day period will have at least one day without rain?

Answer 1

Over 3 days period, either it will not rain for 3 days or at least one day will be without rain. Thus

1= probability that it will not rain for 3 days + probability at least one day will be be without rain.

If it rains for 3 days, this means it rains on day 1 AND it rains on day 2 AND it rains on day 3. The probability that it rains is 68%=.68 and in probability AND means to multiply. So the probability that it rains for all days in 3 days is .68*.68*.68=0.68^3

Then substituting above we have

1= probability that it will not rain for 3 days + probability at least one day will be be without rain.

1=0.68^3+ probability at least one day will be be without rain

probability at least one day will be be without rain=1-0.68^3 which comes out to me about 69%