Did it rain?

Probability Level 2

In a city, Angelica has a 60% of chance to be late for her work if it rains. If it doesn't, she has only a 30% of chance to be late for her work.

One day Angelica saw on the TV that there was 25% of chance of rain on that day.

Knowing that Angelica did not arrive late at her work on that day, what is the probability that it rained that day?

16 % 75% 18% 24% 25%

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Relevant Wiki: Bayes' Theorem

By the Bayes' Theorem we have:

P(rained|not late) = P(rained and not late) P(not late) \displaystyle{\text{P(rained|not late)}=\frac{\text{P(rained and not late)}}{\text{P(not late)}}}

P(rained|not late) = P(rained) x P(not late|rained) P(rained) x P(not late|rained) + P(not rained) x P(not late|not rained)) \displaystyle{\text{P(rained|not late)}=\frac{\text{P(rained) x P(not late|rained)}}{\text{P(rained) x P(not late|rained) + P(not rained) x P(not late|not rained))}}}

P(rained|not late) = 25 % × 40 % 25 % × 40 % + 75 % × 70 % \displaystyle{\text{P(rained|not late)}=\frac{25 \% \times 40 \%}{25 \% \times 40 \% + 75 \% \times 70 \%}}

P(rained|not late) = 1000 % % 6250 % % \displaystyle{\text{P(rained|not late)}=\frac{1000 \% \%}{6250 \% \%}}

P(rained|not late) = 0.16 = 16 % \displaystyle{\text{P(rained|not late)}=0.16=\boxed{16 \%}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...