ruth lives in a place where it rains an average of 12 days out of 90. if the weather each day is independent of the previous day's weather, what is the probability that it will not rain 3 days in a row? round to the nearest whole percent

Question

Mathematics

Boy

4 September, 01:34

ruth lives in a place where it rains an average of 12 days out of 90. if the weather each day is independent of the previous day's weather, what is the probability that it will not rain 3 days in a row? round to the nearest whole percent

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Camilla Medina · Answer 1

65%

Step-by-step explanation:

Probability that it rains is 12/90

So, probability that it will NOT RAIN is 90 - 12 = 78 out of 90

Independent probability gets multiplied, so probability that it will not rain in 3 consecutive days would be:

P (Not Rain) * P (Not Rain) * P (Not Rain)

First, probability of not raining is 78/90, so:

P (Not Rain) * P (Not Rain) * P (Not Rain)

= 78/90 * 78/90 * 78/90 = 474552/729000

When divided, this will be 0.6509

To convert it to percentage, we multiply by 100:

0.6509 * 100 = 65.09

Rounded to nearest percentage, that will be 65%