WTVX$,$ Channel $6,$ is located in Eugene, Oregon, home of

the University of Oregon. The station was owned and operated

by George Wilcox, a former Duck $($University of Oregon

football player$).$ Although there were other television

stations in Eugene, WTVX was the only station that had a

weatherperson who was a member of the American Meteorological

Society $($AMS$).$ Every night, Joe Hummel would be

introduced as the only weatherperson in Eugene who was a

member of the AMS. This was George$$s idea, and he believed

that this gave his station the mark of quality and helped with

market share.

In addition to being a member of the AMS, Joe was the

most popular person on any of the local news programs. Joe

was always trying to find innovative ways to make the weather

interesting, and this was especially difficult during the winter

months, when the weather seemed to remain the same over long

periods of time. Joe$$s forecast for next month, for example, was

that there would be a $70\%$ chance of rain every day and that

what happens on one day $($rain or shine$)$ was not in any way

dependent on what happened the day before.

One of Joe$$s most popular features of the weather report

was to invite questions during the actual broadcast.

Questions would be phoned in$,$ and they were answered on

the spot by Joe. Once a $10-$year$-$old boy asked what caused

fog, and Joe did an excellent job of describing some of the

various causes.

Occasionally, Joe would make a mistake. For example, a

high school senior asked Joe what the chances were of getting $15$

days of rain in the next month $(30$ days$).$ Joe made a quick calculation:

$170\%2*115$ days$>30$ days$2=170\%211>22=35,.$

Joe quickly found out what it was like being wrong in a university

town. He had over $50$ phone calls from scientists, mathematicians,

and other university professors, telling him that he had

made a big mistake in computing the chances of getting $15$ days

of rain during the next $30$ days. Although Joe didn$$t understand

all of the formulas the professors mentioned, he was determined

to find the correct answer and make a correction during a future

broadcast.

Discussion Question

$1.$ What are the chances of getting $15$ days of rain during the

next $30$ days?

$2.$ What do you think about Joe$$s assumptions