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)