I have the answers, but can you please show the steps to get to these solutions?

A box has 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? Answer: 0.8489

b) Ray removes a ball at random from the box, observes the 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? Answer: 0.9693

Hint: Use Bayes' Theorem