1). Flipping a coin or picking a number are not dependent. The probability
of the result is the same every time. It only changes if you leave out what
you picked the first time, because then the total number of possibilities is
different.
With this reasoning, they might say that iii. is dependent because you
don't replace what you draw the first time. I'm not comfortable with that.
Sure, you don't replace the first number you picked, but how many odd
numbers are left ? Still an infinite number.
So I think iii. is the answer they want here, but I don't think any of the
choices is really dependent.
2). By the same reasoning, i. and ii. are independent. The coins have
no memory. They don't remember what happened last time.
3). The probability of any result is
(number of successes)/(number of possibilities).
Total number of possibilities each time is 8.
Probability of an even number (2, 4, 6, or 8) the first time = 4/8 = 0.5
Probability of an odd number (1, 3, 5, or 7) the second time = 4/8 = 0.5
Probability of an 8 the third time = 1/8 = 0.125 .
Probability of all 3 events = (0.5) x (0.5) x (0.125) = 0.03125 (3.125%)
