The probability that it rains on one of 7 days = 1-probability that it does not rain on any of the 7 days.
probability for not raining on any of the 7 days = \((1/2)^7 = \frac{1}{2^7}\)
ans = \(1 - \frac{1}{2^7}\)
or, \(\frac{(2^7 - 1)}{2^7} = \frac{127}{128}\)
_________________

Explanation

Since Quantity A is an “at least” problem, use the 1 – x shortcut. Rather than calculate the probability of rain on exactly 1 day next week, and then the probability of rain on exactly 2 days next week, and so on (after which you would still have to add all of the probabilities together!), instead calculate the probability of no rain at all on any day, and then subtract that number from 1.

That will give the combined probabilities for any scenarios that include rain on at least 1 day. Probability of NO rain for any of the 7 days =\(\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{128}\)

Subtract this probability from 1: \(1-\frac{1}{128}=\frac{127}{128}\).

Quantities A and B are equal.
_________________

Answer: D
Set = {x+1, x+2, x+3, …., x+35}

A: The probability for selecting an even number less than median:
The median is (35-1)/2+1 = 18th which is x+18
Numbers before median are: x+1, x+2, …, x+17 there are 17 numbers before median, and as 17 is not even, we don’t know there are either 9 or 8 even numbers.
A would be either 9/35 or 8/35

B: The probability for selecting an odd number greater than median:
The median is (35-1)/2+1 = 18th which is x+18
Numbers after median are: x+19, x+19, x+20, …, x+35, there are 17 numbers after median, we don’t know there are either 9 or 8 even numbers.
B would be either 9/35 or 8/35

We don’t know the first number in the sequence is even or odd, if we knew we were sure what situation would happen.
Answer is D
_________________

It is said that the probability of raining at any given day next week is 1/2. SO why you took 1/2 for no raining day. I'm confused here. please clarify.
_________________

If, for example, P(rain in Monday) = 0.5, then P(NO rain on Monday) = 1 - 0.5 = 0.5

Likewise, if it were the case that P(rain in Monday) = 0.3, then P(NO rain on Monday) = 1 - 0.3 = 0.7, etc.

Does that help?

Cheers,
Brent
_________________

yes, thank you so much.
_________________