If the chances of rain are 40% and 20% for the two days of the weekend, what is the chance that it will rain on at least one of the two days?

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Answer 1 · 2016-07-18T13:42:57

The Reqd. Prob. $=52%$

Let $D_1=$ the event that it will rain on the first of the given two days of the weekend, and, similar notation for $D_2$ .

Therefore, by what is given, we have,

$P(D_1)=40%=0.4. P(D_2)=0.2$

The Reqd. Prob. $=P(D_1uuD_2)=P(D_1)+P(D_2)-P(D_1nnD_2)$

$=0.4+0.2-P(D_1nnD_2)$

As regards, $P(D_1nnD_2)$ , let us note that the events $D_1 and D_2$ are independent, and as such, we have,

$P(D_1nnD_2)=P(D_1)*P(D_2)=0.4*0.2=0.08$

Therefore,

The Reqd. Prob. $=0.4+0.2-0.08=0.52=52%$

Answer 2 · 2016-07-18T13:43:50

We first look at the chance of it NOT raining at both days.

Saturday: 60% of NO rain, translates to a fraction of $60/100=0.6$
Sunday: 80% of NO rain, a fraction of $80/100=0.8$

Both Sat AND Sun No rain means MULTIPLY :

$P(sat)xxP(sun)=0.6xx0.8=0.48or 48%$

So the chance of rain on at least one of the days will be:
$P=(100-48)%=52%$

Extra:
Of this $P=52%$ there is a chance of
$P=0.4xx0.2=0.08=8%$ that it will rain on both days.

Summary:
- No rain at all: 48%
- Rain one day: 44%
- Rain both days: 8%
Adding up to 100% (this is to check your answer)