probability

Question

John keeps a weather chart. He records each day as either wet or dry.
 If it is dry one day, the probability that it will be dry the next day is 4/5 If it is wet one day, the probability that it will be wet the next day is 2/5 The 31st March is dry.Calculate the probability that at least one of the days, 1st and 2nd April, will be dry

Answer 1

Mar 31  April 1     April 2

 

DRY    W (1/5)     W (2/5)       This combination is both April 1 & 2 are wet*

                          D (3/5)        ⇐This probability is 3/25

          D (4/5)    D (4/5)        ⇐This probability is 16/25

                          W (1/5)       ⇐This probability is 4/25

 

The total of the three probabilities that are shown in BOLD is your answer, 23/25.