Q: A Math quiz has  multiple-choice questions, each with  choices. A student passes the quiz with  or more correct questions. If the student randomly picks their answers, what is the probability of passing the quiz?

A: 7/27  = 1/27 + 6/27
Scenario 1: The student gets all 3 correct (1/3) x (1/3) x (1/3) = 1/27
Scenario 2: The student gets 2 correct.  1/3 x 1/3 x 2/3 but this can happen 3 different ways as the student could get the 1st one incorrect or the 2nd or the 3rd.
so (1/3)x (1/3) x (2/3) x 3 = 6/27
1/27 + 6/27 = 7/27.

Q: If you only have 4s and 5s to make other numbers (such as 4 + 4 + 5 = 13 and 5 + 5 + 5 + 5 + 5 = 25),  how many numbers from 1 to 1000 have this property ?

A: 994
Which #s cannot be made?  There are 6 numbers that cannot be made:1 2 3 6 7  or 11.
That leaves 994 numbers.
All others can be made from 4s and 5s as 8 is 2 4s and 9 is 4 and 5 and 10 is 5 and 5.
After 12 which is 3 x 4, all other numbers can be made.
See above for 13, 14 is 9+5, 15 is 3 5s, 16 is 4 4 s 17 is 12 +5, 18 is 14 + 4, 19 is 15 +4 and so on and so on…