Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4,1/2,5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

The questions states that the probabilities are individual, this means that the success of either of Xavier, Yvonne or Zelda is independent of the other.

The word "and" in probability refers to the mathematical operation "×".

So, Let P represent the probability of something. The question can be rephrased as "What is the probability that Xavier will solve the problem, Yvonne will solve the problem, and Zelda will not solve the problem?"

P(Zelda will not solve the problem) = 1 - P(Zelda will solve the problem)

P(Zelda will not solve the problem) = 1 - [tex]\frac{5}{8}[/tex] = [tex]\frac{3}{8}[/tex]

So, the probability that Xavier will solve the problem, Yvonne will solve the problem, and Zelda will not solve the problem = P(Xavier will solve the problem) × P(Yvonne will solve the problem) × P(Zelda will not solve the problem) = [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{8}[/tex] = [tex]\frac{3}{64}[/tex]