Can any one explain how to solve this problem please??

A three day festival is being planned to be held in a location with the following weather characteristics:

The probability of rain on any given day is 0.14.

If it rains on a particular day then the probability that it also rains on the next day is 0.41.

If it rains for two days in a row then the probability that it will rain on the following day is 0.26.

What is the probability that it will rain on any day during the festival? ____________

What is the probability that it will rain on the second day, but not rain on the first day and not rain on the last day? ____________

I started with defining the sample space of this experiment which contains 8 possibilities S = { NNN,RNN,NRN,NNR,RRN,RNR,NRR,NNN}. To answer the first question, I’ve thought of using the complement of NNN sample point to calculate the probability of at least on rainy day —> 1- P(NNN). Since no mention of conditional probabilities related to this, I assumed that they are independent hencemy answer was 1 - 0.86 ^ 3. For the second question I’ve also assumed the events are independent and my answer was .86^2 x .14. The problem is that when working the probabilities of all 8 sample points in the sample space using the chain rule ( and assuming independence when no conditional probabilites are given), the 8 probabilities don’t add up to 1. I feel that I’m missing something here.

A three day festival is being planned to be held in a location with the following weather characteristics:

The probability of rain on any given day is 0.14.

If it rains on a particular day then the probability that it also rains on the next day is 0.41.

If it rains for two days in a row then the probability that it will rain on the following day is 0.26.

What is the probability that it will rain on any day during the festival? ____________

What is the probability that it will rain on the second day, but not rain on the first day and not rain on the last day? ____________

I started with defining the sample space of this experiment which contains 8 possibilities S = { NNN,RNN,NRN,NNR,RRN,RNR,NRR,NNN}. To answer the first question, I’ve thought of using the complement of NNN sample point to calculate the probability of at least on rainy day —> 1- P(NNN). Since no mention of conditional probabilities related to this, I assumed that they are independent hencemy answer was 1 - 0.86 ^ 3. For the second question I’ve also assumed the events are independent and my answer was .86^2 x .14. The problem is that when working the probabilities of all 8 sample points in the sample space using the chain rule ( and assuming independence when no conditional probabilites are given), the 8 probabilities don’t add up to 1. I feel that I’m missing something here.

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