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You are planning a​ three-day trip to​ Seattle, Washington, in October. Use the fact that on each​ day, it could either be sunny or​ rainy, and that each day is equally likely to be sunny or rainy to answer the following question. What is the probability that it rains on exactly one​ day?

Respuesta :

Answer:

Step-by-step explanation:

In this case, we can put all the scenarios and then, count the scenario which can be rainy at least one day (it doesn't matter if it's day 1, day 2 or day 3 because it's asking for exactly one day). With this, we can also assume that the rest of the days will be sunny so:

We have this scenarios:

S: Sunny

R: Rainy

Now, let's do the scenarios:

If day 1 begins sunny:

SSS, SSR, SRS, SRR

If day 1 begins with Rain:

RRR, RRS, RSR, RSS

So, we have 8 possible scenarios, now let's see which ones we have one day of raining and the rest of the days, are sunny.

SSR, SRS and RSS

We have 3 scenarios, which can be rainy exactly one day.

So the probability is:

3/8 = 0.375 or simply 37.5%

fichoh

Using the binomial probability relation, the probability that it rains on exactly one day is 0.375

Let :

  • Sunny = S
  • Rainy = R

The probability that it rains on exactly one day can be obtained using the binomial probability relation :

  • P(x = x) = nCx * p^x * q^(n-x)

  • Probability of success = p = 0.5
  • n = number of trials = 3
  • q = 1 - p = 0.5

P(x = 3) = 3C1 * 0.5¹ * 0.5²

P(x = 1) = 3 × 0.5 × 0.25

P(x = 1) = 0.375

Therefore, the probability that it rains on exactly one day is 0.375

Learn more : https://brainly.com/question/12474772

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