Rain Or Shine

Probability Level 2

The weather forecast stated that there would be 60% chance of rain on Saturday and 30% chance of rain on Sunday.

What is the probability (in percentage) of rain on at least one of these two days? (Assume the days are independent.)


The answer is 72.

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Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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6 solutions

Let A A be the event of rain on Saturday and B B be the event of rain on Sunday and P P is the probability. Thus, the probability of A A or B B is written as P ( A ∪ B ) P(A \cup B) .

Then similar to the set operation, P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) = 60 % + 30 % − ( 60 % × 30 % ) = 72 % P(A \cup B) = P(A) + P(B) - P(A \cap B) = 60\% + 30\% - (60\%\times 30\%) = 72\% .

As a result, there would be a 72 % \boxed{72\%} chance on rain on Saturday or Sunday.

10 Helpful 0 Interesting 0 Brilliant 0 Confused

You should also state that these are independent variables.

Anton Hirschowitz - 5 years ago

Your explanation is the best way to look at it, a simple problem.

Patricia Acord - 5 years ago
J D
May 31, 2016

There is a 60% chance of rain on Saturday. There is a 40% chance of no rain on Saturday, but a 30% chance of rain on Sunday. The chance of rain on Sunday is only relevant if it doesn't rain on Saturday, so the probability is 60% + 40% x 30% =72%.

9 Helpful 0 Interesting 0 Brilliant 0 Confused

The question is poorly phrased. Your solution describes the following question:

What is the probability of rain on Sunday if it doesn't rain on Saturday?

Paul Becker - 5 years ago

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Paul Becker, not really. The probabilty that is rains on Sunday is independend from whether there was rain on Saturday or not, it is always 30%.

The phrasing of the questionis fine, there is only one distinct way to interpret it.

Kai Ott - 5 years ago

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I agree with Paul Becker, the wording could be better to clearly show the dependence that he talks about in the solution

Ben Barrass - 5 years ago
Kai Ott
Jun 1, 2016

The probability that it rains on either Sunday or Saturday or on both days can be expressed as 1 - the probability that it doesn't rain on both, Saturday and Sunday (complementary event).

So the answer is 1 - (1 - 0.6) × (1 - 0.3) = 1 - 0.28 = 72%.

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Sharky Kesa
Jun 6, 2016

An easy way to solve this question is to take the complement, that is to find the probability it won't rain at all during the weekend. But this is simply 40 % × 70 % = 28 % 40\% \times 70 \% = 28\% . Thus, the probability of it raining must be 72 % 72\% .

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Justin Malme
Jun 2, 2016

The odds of it raining either Sat or Sun = 1 - (the odds of it NOT raining either day).
The odds of it NOT raining on Sat = 40% = 4/10.
The odds of it NOT raining on Sun = 70% = 7/10.
The odds of it NOT raining both days = 4/10 X 7/10 = 28/100.
Therefore, The odds of it raining either Sat or Sun = 1 - (the odds of it NOT raining either day) = 1 - (28/100) = 72/100 = 72%.



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Angus Johnson
Jun 1, 2016

I really dislike that it makes you write the answer as 72. 72% = 0.72 but these are not equal to 72. 72 is not a probability.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

It is stated "probability of rain (in percentage)". So, it is 72 percentage.

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Calvin Lin Staff - 5 years ago

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