Two balls are drawn in succession out of a box containing
4 red and 4 white balls. find the probability that at least 1 ball was red, given that the first ball was

a. replaced before the second draw.

b. not replaced before the second draw

There are a total of 8 balls 

The probability of drawing a white ball is 4/8 on the first draw.
If you replace the ball then the probability will still be 4/8 for a white ball, since these events are independent of each other you multiply 4/8 x 4/8 = 16/64 or 1/4 then the probability of drawing at least 1 red ball with replacement is 1 - 1/4 = 3/4

Now without replacement:
the probability of drawing a white ball is 4/8 since you don't replace the ball then the probability of drawing a white ball the second time is 3/7 again multiply these two probabilities: 4/8 x 3/7 = 12/56 the the probability of drawing at least 1 red ball is 1- 12/56 = 44/56 or 11/14