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Chapter 2

Probability concepts & Applications

Solution to Case study

Probability of r successes in n trials

Thus, the probability of getting 15 days of rain in the next 30days is 1.06%.

We want to find the probability of getting 15 days of rain during the next 30 days.

Thus, the chance of rain every day is 70%, and that what happens on one days (rain or shine) was not in any way dependent on what happened the day before.

1. What are the chances of getting 15 days of rain during the next 30 days?

In this case;

n =number of days = 30

r= number of rainy days = 15

p = probability of rain = 70% = 0.70

q = 1-p = 1- 0.70 = probability of sun = 30% = 0.30

WTVX was the only station that had a weatherperson who was the member of the Amarican Meteorological Society (AMS) - Joe Hummel - who was always trying to find innovative ways to make weather interesting by inviting questions during the actual broadcast

Case study

Binomial distribution

=> Binomial formula

Probability of r successes in n trials =

n = number of trials

r =number of successes

p = the probability of success on any single trial

q = 1 – p = the probability of a failure

2. What do you think about Joe’s assumptions concerning the weather for the next 30 days?

WTVX, Channel 6, located in Eugene, Oregon, home of the University of Oregon's football team

The two variables are exactvalue, for example given that one apple costs 10 NTD, so 2 apples cost 20 NTD. But this case is talking about chance which is not exact value. It means the probability of rain today is perhaps 80% as opposed to 70%. Thus, Joe should concern that this is the probability. He should think about the probability methods and 70% chance of rain every day doesn’t depend on the day before.

- Joe’s assumption that the chance of getting 15 days of rain in the next 30 days (35%) is wrong. He uses the rule of the rule of three. This method is to find the fourth term of a mathematical proportion when three terms are known. It is based on the principle that the product of the first and fourth terms (called the extremes) is equal to the product of the second and third terms (called the means).

Joe's quick caculation:

(70%) * (15 days/ 30 days)

= (70%) * (1/2)

= 35%

Sajeena Vivatbutsiri _ G1022241301

Mayy Nguyen _ G1022241009

Joe's mistake

What the chances were of getting 15 days of rain in the next month (30 days), if there would be a 70% chance of rain everyday, and that what happens on one day (rain or shine) was not in any way dependent on what happened the day before?

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