Answer:

Telly and Carey were already hard at work when Ms. Kelley came into the bike shop on Thursday morning. It was three days before the big race and there was still a lot of work to be done.

“I can’t believe it!” Ms. Kelley exclaimed as she came into the shop.

“What?” both girl asked alarmed.

“There is a 4 to 5 chance that it is going to rain on Saturday. I just heard the weather report,” Ms. Kelley said sighing.

“Well, there is still a chance that it won’t,” Telly said trying to cheer her up.

When we think about chances and odds, we can calculate the likelihood that an event will or won’t occur. In this case, there are odds that it will rain and odds that it won’t. We can also express those odds as a fraction or a percentage. Learn about odds in this reading, and you can work on the odds of the rainstorm at the end.

Guidance

You’ve seen that the probability of an event is defined as a ratio that compares the favorable out comes to the total outcomes. We can write this ratio in fraction form.

P

(

event

)

=

favorable outcomes

total outcomes

Sometimes people express the likelihood of events in terms of odds rather than probabilities. The odds of an event occurring are equal to the ratio of favorable outcomes to unfavorable outcomes.

A spinning wheel split into three equal parts: one part red, one blue, and one yellow.

Think about the odds for the arrow of the spinner above landing on red:

favorable outcomes = 1(red)

unfavorable outcomes = 2(blue, yellow)

total outcomes = 3

So the probability of spinning red is:

P

(

red

)

=

favorable outcomes

total outcomes

=

1

3

While the odds in favor of red are:

Odds(in favor of red)

=

favorable outcomes

unfavorable outcomes

=

1

2

Odds against an event occurring are defined as:

Odds(against red)

=

unfavorable outcomes

favorable outcomes

=

2

1

You can solve any probability problem in terms of odds rather than probabilities. Notice that the ratio represents what is being compared. Be sure that your numbers match the comparison.

We can use odds to calculate how likely an event is to happen. We can compare the odds in favor of an event with the probability that the event will actually occur. Let’s look at an example.

Take a look at this situation.

You’ve seen that the odds in favor of an event (E) occurring are shown in this ratio.

Odds(in favor of)

E

=

favorable outcomes

unfavorable outcomes

=

1

2

And the odds against the same event occurring are:

Odds(against)

E

=

unfavorable outcomes

favorable outcomes

=

2

1

You can use these two facts to compute the ratio of things happening and not happening.