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 15% chance of rain on the first day, a 10% chance of rain on the second day, a 20% chance of rain on the third day, a 20% chance of rain on the fourth day, and a 60% 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.

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joaobezerra joaobezerra · Answer 1 · 2019-10-10T15:43:10+02:00

Answer:

There is a 19.58% probability that it does not rain during the entire festival.

Step-by-step explanation:

We have these following probabilities:

On the first day, a 15% chance of rain. So an 85% chance of not raining.

On the second day, a 10% chance of rain. So a 90% chance of not raining.

On the third day, a 20% chance of rain. So an 80% chance of not raining.

On the fourth day, a 20% chance of rain. So an 80% chance of not raining.

On the fifth day, a 60% chance of rain. So an 40% chance of not raining.

What is the probability that it does not rain during the entire festival?

We have to multiply the probability that it does not rain on each day. So

[tex]P = 0.85*0.90*0.80*0.80*0.40 = 0.1958[/tex]

There is a 19.58% probability that it does not rain during the entire festival.