Mathematicians PLS HELP me OUT!!?

Question

1. We pull two numbers out of {1; 2; 3; 4; 5; 6; 7; 8}: What is the probability that the product of the two
numbers pulled is odd? Assume
(a) replacement.
(b) no replacement
2. We pull two numbers out of {1; 2; 3; 4; 5; 6; 7; 8}. What is the probability that we pull the numbers
in an increasing order? Assume
(a) replacement
(b) no replacement.

Pls Explain and show workings

Answer 1

product will be odd if and only if each of the numbers is odd

p = (4/8)^2 = 1/4 with replacement
p = 4/8 * 3/7 = 3/14 without replacement

second is more complicated
we pick a first number (1/8) and the status of the next depends on which one we picked first
1/8 * 7/8 + 1/8*6/8 + .+1/8* 1/8 = 1/8 * (7*8/2)/8 = 7/16 repl
1/8 * 7/7 + 1/8*6/7+ + 1/8*1/7 = 1/8*(7*8/2)/7 = 1/2 without rep

Answer 2

1. In order for the product of two numbers to be odd, the two numbers should be odd.

(a) with replacement the probability to choose twice one odd number out of 4 is (4/8)^2 = 1/2^2 = 1/4

(b) No replacement: the probability for the first number to be odd is 1/2, and for the second, provided the first is odd is 3/7, the overall probability is 1/2 * 3/7.

2. Here, we have the following possibilities to select two numbers in increasing order:
(1,2),(1,3)...,(1,8)
(2,3),...,(2,8)
.
.
.
(7,8)
The number of such possibilities is: 1+2+...+7 = (1 + 7)*3.5 =
= 28

(a) we select those possibilities out of 8*8=64, and the probability is 28/64 = 7/16

(b) With no replacement we select first out of 8 numbers, and then out of 7, i.e. out of 8*7=56 possibilities to draw two numbers.
The probability is 28/56 = 1/2

Answer 3

Do you want this answer because you are interested in math and want to learn a certain topic, or do you need your math homework done? Were you not paying attention in class? I don't think you should be cheating on that homework of yours ;-).

PS- I'm in 7th grade and I can figure it out