Suppose that in a recent (2017) hurricane season, there were 8 tropical storms,

Question

Suppose that in a recent (2017) hurricane season, there were 8 tropical storms, 6 minor hurricanes (Level 1), and 6 major hurricanes (Level 2 or higher) observed in the tropical Atlantic (as defined by the highest level of event intensity for each of these 20 independent events that were tracked). As a regional climatologist, you wish to sample from this population of N=20 events to analyze wind and rainfall patterns. You decide to randomly sample n=10 events from the N=20 events using a sampling without replacement framework to avoid redundancy. Calculate the probability that less than 3, but at least one, of the 10 randomly selected events is a tropical storm.

Explanation / Answer

Answer to the question)

P(tropical) = 8/20 = 0.40

Total observations = n = 10

P(1 = < x < 3) = P(x=1) + P(x=2)

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Formula of Binomial Probability:

P(X=x) = nCx * p^x * (1-p)^(n-x)

P(x=1) = 10C1 * (0.40)^1 * (0.60)^9 = 0.0403

P(x=2) = 10c2 * (0.40)^2 * (0.60)^8 = 0.1209

P(x = 1, 2) = 0.0403 + 0.1209

P(x=1,2) = 0.1612

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