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

Answer 1

The probability that it will not rain for the next two weeks is 0.68 when calculated using the given probabilities of no rain for this week and next week.

Step-by-step explanation:

To calculate the probability that it will not rain for the next two weeks, we will use the probabilities given for rain this week and next week, both when it does and does not rain this week. Using the provided tree diagram information: the probability of no rain this week (P(No Rain This Week)) is 0.80, and the probability of no rain next week if it does not rain this week (P(No Rain Next Week|No Rain This Week)) is 0.85.

To find the total probability of no rain for both weeks, we multiply these probabilities together:

P(No Rain This Week and Next Week) = P(No Rain This Week) × P(No Rain Next Week|No Rain This Week)

P(No Rain This Week and Next Week) = 0.80 × 0.85 = 0.68

Therefore, the probability that it will not rain for the next two weeks is 0.68, or 68% when expressed as a decimal precise to two decimal places.

Answer 2

the probability that it will not rain for the next two weeks is approximately 0.82, expressed as a decimal precise to two decimal places.

Let's find the probability:

To find the probability that it will not rain for the next two weeks, we need to consider both the scenarios where it doesn't rain this week and next week, and the scenario where it rains this week but doesn't rain next week.

Probability of no rain this week and next week:

This is simply the product of the probability of no rain this week (0.8) and the probability of no rain next week given no rain this week (0.85).

So, the probability of this scenario is 0.8 * 0.85 = 0.68.

Probability of rain this week and no rain next week:

This is the product of the probability of rain this week (0.2) and the probability of no rain next week given rain this week (0.69).

So, the probability of this scenario is 0.2 * 0.69 = 0.138.

Finally, to get the overall probability of no rain for the next two weeks, we need to add the probabilities of the two scenarios we just calculated:

Probability of no rain for the next two weeks = 0.68 + 0.138 = 0.818.