Suppose a weather report indicates that the probability of rain this week is 0.2

Question

Suppose a weather report indicates that the probability of rain this week is 0.20. According to the report, if it rains this week, then the probability of rain next week is 0.31. If it does not rain this week, then the probability of rain next week is 0.15. The tree diagram models this weather report. This week Next week Rain Determine the probability that it will not rain for the next two weeks. Express your answer as a decimal precise to two decimal places Rain 0.15 0,80 probability = No rain 0.85 No rain

Explanation / Answer

Using the tree diagram,

The event where it does not rain for the next two weeks is (No rain, No rain) which is the lowermost branches of the tree.

Probability is 0.80 * 0.85

= 0.68.

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