How to answer and answer In New Hampshire, there is a sunny day about once every 2 days. When it is sunny out, Alan skips class about 65% of the time. When it isnot sunny out, Alan skips class about 40% of the time. What is the probability that it is sunny out when Alan skips class? (Enter theprobability as a decimal rounded to four decimal places.)

Consider: A=event that represents the day is sunnyB=event that represents that Alan skips the class We are given that, P(day is sunny)=P(A)=12=0.5P(Alan skips the class when day is sunny)=P(B/A)=65%=0.65P(Alan skips the class when day is not sunny)=P(B/Ac)=40%=0.40We know that Ac represents that the day is not sunny. Its probability is shown as follows: P(Ac)=1-P(A) =1-0.5 =0.5Now, we need to find the probability that it is sunny out when Alan skips class, i.e, P(A/B) by using the Bayes Theorem. The calculations are shown as follows: P(A/B)=P(B/A)×P(A)P(B/A)×P(A)+P(B/Ac)×P(Ac) =0.65×0.50.65×0.5+0.40×0.5 =0.3250.325+0.2 =0.3250.525 =0.619047619 ≈0.6190 Hence, the probability that it is sunny out when Alan skips class is equal to 0.6190.