Question

A local weather forecast states that the probability of rain on Saturday is 80%. What are the odds that it will not rain Saturday?
a) $1:2$
b) $1:3$
c) $1:4$
d) $1:5$

Answer 1

Answer:

$1:4$

Step-by-step explanation:

$\text{Solution:}\\\text{Given:}\\\text{Probability of rain on Saturday}(p)=80\%=\dfrac{80}{100}=0.8\\\text{Probability of no rain on Saturday }(q)=?\\\text{Now,}\\\text{Probability of rain on Saturday }(q)=1-p=1-0.8=0.2$

$\text{To convert the probability to odds:}\\\text{Odds of no rain = Probability of no rain}\div\text{Probability of rain}\\\text{}\qquad\qquad\qquad\quad\text{= 0.2}\div0.8=\dfrac{2}{8}=\dfrac{1}{4}=1:4$

p = 1 - q is known as the compliment rule, which states that the probability that an event does not occur is 1 minus the probability that event occurs.

Answer 2

Final answer:

The odds that it will not rain on Saturday, given an 80% probability of rain, are 1:4, meaning for every chance of it not raining, there are four chances of it raining. So the correct answer is option C.

Explanation:

The question asks for the odds that it will not rain on Saturday given that the probability of rain is 80%. The probability of it not raining is the complement of the probability of rain.

Which is 100% - 80% = 20%. The odds are the ratio of the probability that an event will occur to the probability that it will not.

So, the odds for it not to rain are 20% to 80%, which simplifies to 1:4, because the 80% chance of rain is four times the 20% chance of it not raining. Hence, the correct answer is (c) 1:4.