You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during

Question

12 days ago

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You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during

the festival, but the weather forecast says there is a 45% chance of rain on the first day, a 55% chance of rain on the second day, a 10% chance of rain on the third day, a 10% chance of rain on the fourth day, and a 5% chance of rain on the fifth day. Assume these probabilities are independent of whether it rained on the previous day or not. What is the probability that it does not rain during the entire festival? Express your answer as a percentage to two decimal places.

Mathematics

1 answer:

zzz [11.8K] · Answer 1 · 2026-03-28T10:23:58+03:00

Answer:

The chance of remaining dry throughout the whole festival is 0.19

Step-by-step explanation:

According to the Complement Rule, the aggregate of the probabilities of an event and its opposite is always equal to 1.

Here, we consider the likelihood of rain each day, so we need to find the chances of it NOT raining.

On the first day, there's a 45% possibility of rain; thus, the complement is 55%

On the second day, the chance of rain is 55%, making its complement 45%

For the third day, the likelihood is 10%, giving a complement of 90%

On the fourth day, the rain chance remains 10%, so the complement stays at 90%

The fifth day presents a 5% chance of rain, resulting in a complement of 95%

To determine the probability of not encountering rain for the entire festival, we multiply all the complements.

P(not raining) = 0.55 x 0.45 x 0.90 x 0.90 x 0.95= 0.19