Question

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? % (round to 2 decimal places)

Explanation:

Step1: Calculate the probability of no - rain for each day

The probability of no - rain on the first day: \(P(\text{no rain}_1)=1 - 0.15=0.85\)
The probability of no - rain on the second day: \(P(\text{no rain}_2)=1 - 0.10 = 0.90\)
The probability of no - rain on the third day: \(P(\text{no rain}_3)=1 - 0.20=0.80\)
The probability of no - rain on the fourth day: \(P(\text{no rain}_4)=1 - 0.20 = 0.80\)
The probability of no - rain on the fifth day: \(P(\text{no rain}_5)=1 - 0.60=0.40\)

Step2: Use the multiplication rule for independent events

Since the events (no - rain on each day) are independent, the probability that it does not rain during the entire festival is \(P = P(\text{no rain}_1)\times P(\text{no rain}_2)\times P(\text{no rain}_3)\times P(\text{no rain}_4)\times P(\text{no rain}_5)\)

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Step3: Convert to percentage and round

To convert to a percentage, we multiply by \(100\). So \(P = 0.19584\times100\%=19.584\%\)
Rounding to two decimal places, we get \(19.58\%\)

Answer:

\(19.58\%\)