Question

in a beach side suburb it rains on 20% of days and is windy on 30% of days. if rain and wind are independent, on any particular day find the probability that:
(a) it rains and is windy (b) it does not rain and is not windy (c) it rains or it windy (d) it does not rain or is not windy

Answer 1

Start with a table:
R=rain (20%), ~R=no rain (80%)
W=windy (30%), ~W=not windy (70%)

If rain and wind are independent, the combined occurrence is the product of the respective probabilities.
Example:
(a)P(R∧W)=.2*.3=0.06
(b)P(~R∧~W=0.8*0.7=0.56
(c)...
Will leave (c) and (d) for you as exercise.

Answer 2

(a) .20 * .30 = .06
(b) (1-.20) * .30 = .24
(c) .20 + .30 - .20*.30 = .44
(d) (1-.20) + (1-.30) - (1-.20)(1-.30) = .94

Note that (d) = 1-(a)

Answer 3

Oops. I misread (b). My answer is ~rain & windy