A total of 12 cells are replicated. Freshly synthesized DNA cannot be replicated again until mitosis is completed. Two control mechanisms have been identified—one positive and one negative—that are used with equal probability. Assume that each cell independently uses a control mechanism. Determine the following probabilities.

(a) All cells use a positive control mechanism.

(b) Exactly half the cells use a positive control mechanism.

(c) More than four but fewer than seven cells use a positive control mechanism.