Tree diagram with two levels of branches for all of the outcomes. The first leve

Question

Tree diagram with two levels of branches for all of the outcomes. The first level of branching is for week 1 outcomes, and starts as two branches, with the top branch identified as snow this week, with probability of 0.30, and the bottom branch identified as no snow this week, with probability of 0.70. The second level of branches displays two branches for each of the outcomes for this week. The branches stemming from the snow outcome from this week show a top branch for snow next week with conditional probability of 0.39, and a bottom branch for no snow next week with conditional probability of 0.61. The branches stemming from the no snow outcome from this week show a top branch for snow next week with conditional probability of 0.21, and a bottom branch for no snow next week with conditional probability of 0.79. Suppose a weather forecast reports that the probability of snow this week is 0.30. The forecast states that if it snows this week, the probability that it snows next week is 0.39. If it does not snow this week, the probability that it snows next week is 0.21. The tree diagram depicts the possible weather event outcomes with the associated probabilities. What is the probability that it will snow next week? Provide your answer with precision to two decimal places.

Explanation / Answer

Probabilty of snow this week, P(S1) = 0.30

Probabilty of no snow this week, P(NS1) = 0.70

Probabilty of snow Next week when it snowed this week, P(S2) = 0.39

Probabilty of snow Next week when it did not snowed this week, P(S3) = 0.21

Probability that it will snow next week = P(S1)*P(S2) +P(NS1)*P(S3)

= 0.30*0.39 + 0.70*0.21

= 0.117 + 0.147

= 0.264 = 0.26

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