Chocoholic Inc. produces boxes of chocolate bars, where 40% of the chocolate bars in each box are dark chocolate and the remainder of the bars are milk chocolate. From a box of 20 chocolate bars, 5 bars are selected without replacement. Let X represent the number of dark chocolate bars selected. 3 decimal precision please. Note that you can enter scientific notation as 5.32e-3 for 0.00532. a. Calculate P(X = 3). Number b. What is the probability of selecting exactly 2 bars of the same flavour (either milk or dark) while the remaining bars selected are the other flavour? Number c. Calculate P(X =3) if the chocolate bars were selected with replacement. Number Use the following information for parts d. and e.: To fill the boxes, Chocoholic Inc. has two huge (essentially infinitely full) bins of milk and dark chocolate bars, respectively. They hire an employee who takes a bar out of a bin at random (each flavour has equal probability of being selected) and puts it in the box until the box is full with 20 bars. d. Consider two boxes filled using this method. What is the probability that at least one of them has the correct number of dark chocolate (40%) and milk chocolate (60%) bars? Number e. Find the probability that the employee fills at least 3 boxes incorrectly before filling a box with the correct number of dark and milk chocolate bars? Number