Please show all work and label steps clearly so I can follow exactly what you're doing and the process you use! I believe I'm supposed to use binomial probability to solve here but having difficulty. Thank You!

Suppose a box contains 4 red and 4 blue balls. A ball is selected at random and removed, without observing its color. The box now contains either 4 red and 3 blue balls or 3 red and 4 blue balls.

a. Nate removes a ball at random from the box, observes its color and puts the ball back. He performs this experiment 6 times and each time the ball is blue. What is the probability that a red ball was initially removed from the box?

b. Ray removes a ball at random from the box, observes its color and puts the ball back. He performs this experiment 84 times. Out of these, the ball was blue 48 times and red 36 times. What is the probability that a red ball was initially removed from the box?