Find the probability that a cell stains properly.
Further study of the cell-staining problem (Exercises 29 and 30) reveals that new cells stain properly with probability 0.95, 1-day-old cells stain properly with probability 0.9, 2-day-old cells stain properly with probability 0.8, and 3-day-old cells stain properly with probability 0.5. Suppose
Pr(cell is 0 day old) = 0.4
Pr(cell is 1 day old) = 0.3
Pr(cell is 2 days old) = 0.2
Pr(cell is 3 days old) = 0.1.