Question

The probability that it will rain today is 50%. The probability that it will rain tomorrow is 40%. Assuming today and tomorrow’s precipitation outcomes are independent from one another, what is the percent probability that it will rain on at least one of the two days? Express your answer as a whole number.

Answer 1

Consider this option:
1. if suppose, that probability for the rain today is p=0.5, for tomorrow p1=0.4. Then probability for no rain today is q=1-p=0.5, for tomorrow is q1=1-p1=0.6.
2. According to the condition full probability is:
P=p*q1 + p1*q + p*p1=0.5*0.6+0.4*0.5+0.5*0.4=0.3+0.2+0.2=0.7 or 70%.

Note that: p*q1 means 'rain today, no rain tomorrow'; p1*q means 'no rain today, rain tomorrow' and p*p1 means 'rain today, rain tomorrow'.