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

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 50% chance of rain on the first day, a 25% chance of rain on the second day, a 20% chance of rain on the third day, a 5% chance of rain on the fourth day, and a 10% 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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  1. 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.

  2. The probability of not rain during the entire festival is 0.19

    Step-by-step explanation:

    The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1.

    In this case we have the probability of raining of each day,  we need the probability of NOT raining.  

    First day= 45% chance of rain, the complement is 55%

    Second day 55% chance of rain, the complement is 45%

    Third day a 10% chance of rain, the complement is 90%

    Fourth day a 10% chance of rain, the complement is 90%

    Fifth day 5% chance of rain, the complement is 95%

    To get the probability of NOT raining in the entire festival is the multiplication of all the complements.

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

  3. 25.65%

    Step-by-step explanation:

    P(Does not rain during the entire festival)

    = (1 - 0.50)*(1 - 0.25)*(1 - 0.20)*(1 - 0.05)*(1 - 0.10)

    = 0.2565

    = 25.65 %

  4. Probability that it does not rain during the entire festival = 0.19584

    Step-by-step explanation:

    We are given that you and a group of friends are going to a five-day outdoor music festival during spring break.

    Also, Probability that there may be rain on first day, P(A) = 0.15

    Probability that there may be rain on second day, P(B) = 0.10

    Probability that there may be rain on third day, P(C) = 0.20

    Probability that there may be rain on fourth day, P(D) = 0.20

    Probability that there may be rain on fifth day, P(E) = 0.60

    It is also provided that these probabilities are independent of whether it rained on the previous day or not.

    Now, probability that it does not rain during the entire festival = Probability that there may not be rain on all five days

    = (1 - P(A)) [tex]\times[/tex] (1 - P(B)) [tex]\times[/tex] (1 - P(C)) [tex]\times[/tex] (1 - P(D)) [tex]\times[/tex] (1 - P(E))

    = (1 - 0.15) [tex]\times[/tex] (1 - 0.10) [tex]\times[/tex] (1 - 0.20) [tex]\times[/tex] (1 - 0.20) [tex]\times[/tex] (1 - 0.60)

    = 0.85 [tex]\times[/tex] 0.90 [tex]\times[/tex] 0.80 [tex]\times[/tex] 0.80 [tex]\times[/tex] 0.40 = 0.19584

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