Question

In a certain city during the month of May, the probability that a rainy day will be followed by another rainy day is 0.80 and the probability that a sunny day will be followed by a rainy day is 0.60. Assuming that each day is classified as being either a rainy or sunny and that the weather on any given day depends only on the weather the day before, find the probability that in the given city a rainy day in May is followed by two more rainy days, then a sunny day, and finally another rainy day

Answer 1

I so need help on this question

Answer 2

because each day depends on the day before we have to use multiplication between probablities

Answer 3

so lets start with the first one...

Answer 4

A rainy day followed by a rainy day (.8) followed by another rainy day (.8)

Answer 5

if the probablitity of a rainy day following a rainy day is .8 then a sunny day following a rainy day is .2,

Answer 6

So far we have .8*.8*.2

Answer 7

then a rainy day following a sunny day is .6. this leaves us with the anser .8*.8*.2*.6

Answer 8

Understand better now?

Answer 9

Thank you very much
really appreciate the help