# 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?

Jul 18, 2016

The Reqd. Prob.=52%

#### Explanation:

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.$= P \left({D}_{1} \cup {D}_{2}\right) = P \left({D}_{1}\right) + P \left({D}_{2}\right) - P \left({D}_{1} \cap {D}_{2}\right)$

$= 0.4 + 0.2 - P \left({D}_{1} \cap {D}_{2}\right)$

As regards, $P \left({D}_{1} \cap {D}_{2}\right)$, let us note that the events ${D}_{1} \mathmr{and} {D}_{2}$ are independent, and as such, we have,

$P \left({D}_{1} \cap {D}_{2}\right) = P \left({D}_{1}\right) \cdot P \left({D}_{2}\right) = 0.4 \cdot 0.2 = 0.08$

Therefore,

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

Jul 18, 2016

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

#### Explanation:

Saturday: 60% of NO rain, translates to a fraction of $\frac{60}{100} = 0.6$
Sunday: 80% of NO rain, a fraction of $\frac{80}{100} = 0.8$

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%