Question

For this discussion, consider how probability is used in real world scenarios and how they can be solved.

Post a real world probability problem for your classmates to solve. Use normal or binomial distribution within the problem.

Answer 1

One of real world probability problem is weather forecasting. We can see in any weather forecasting sites, there is an information of probability of rain on any particular day or in any particular time period. We use that information to plan our outdoor activities. Let's say that on average based on past data, it will rain on 12 days in the month of September. Thus, the probability of rain on any given particular day in September month is 12/30 = 0.4. Suppose I need to go for a extra classes this whole week (7 days). Let X be the number of days in the week, I expect a rainy day. Then X ~ Binomial(n = 7, p = 0.4)

The problems based on this scenario can be,

What is the probability that I encounter no rainy days in that week?

Ans. P(X = 0) = ⁷C₀ * 0.4⁰ * (1 - 0.4)⁷ = 0.0279936

What is the probability that I encounter 3 rainy days in that week?

Ans. P(X = 3) = ⁷C₃ * 0.4³ * (1 - 0.4)⁴ = 0.290304

What is the expected number of rainy days in a week?

Ans. E(X) = np = 7 * 0.4 = 2.8 days

If today is a rainy day, what is the chance that tomorrow is also a rainy day?

Ans. Since we assume in a Binomial distribution, that all days are independent, the probability of rain next day is independent of today and is equal to p = 0.4