If the probability of rain is 25% on Sat and 25% on Sun, what is the probability that it will rain on one day?

Question

Probability that it will rain on at least one of the two days?

Answer 1

I prefer calculations in decimals.

P(rain on Sat, but not on Sun) = 0.25 x 0.75 = 0.1875
P(rain on Sun, but not on Sat) = 0.75 x 0.25 = 0.1875
P(rain on Sat & Sun) = 0.25 x 0.25 = 0.0625

So the required probability that it rains at least on 1 day is 0.1875 + 0.1875 + 0.0625 = 0.4375, which is equal to 43.75%.

If not, theres a shorter method.

P(does not rain on Sat & Sun) = 0.75 x 0.75 = 0.5625
Hence the required probability is the complement, which is 1- 0.5625= 0.4375 (43.75%) as well.

Answer 2

Plenty of good answers. I just want to point out a couple of things.

Anytime you see that wording 'at least one' it's almost always easier to calculate the compement of that which is 'none' and use
P(at least one) + P(none) = 1

2. Independence is a major feature to look for. It's implyed here. When there is independence then you multiply individual probabilities, in this case the probability of rain on each of the two days.
P(no rain Sat and no rain Sun) = P(no rain Sat)*P(no rain Sun)
= 0.75*0.75 = 9/16 = 0.5625

Thus
P( rain on at least one day ) = 1-0.5625 = 0.4375 (=7/16)

[Do enought of these problems and you'll probably develop a preference for fractions]

Answer 3

the probability is
P=1 - (probability of rain at both days)
= 1 - (0.25 x0.25)

Answer 4

heres the work...

.5/2 = x/7

2x = 3.5/2

x=1.75

1.75/7 = .25 = 25%

25% chance it rains on one day

Answer 5

25%

Answer 6

It's 1 - prob(no rain both days) = 1 - (.75)(.75) = 0.4375

Answer 7

3/16
1/4*3/4

Answer 8

1-Prob(it won't rain on either day)
= 1-0.75*0.75 = 0.4375 = 43.75%