Answer: The probability that Xavier and Yvonne can solve a problem but Zelda cannot is [tex]\frac{3}{64}[/tex]
Step-by-step explanation:
We are given:
Probability of success of Xavier, [tex]P(S)_{Xavier}=\frac{1}{4}[/tex]
Probability of failure of Xavier, [tex]P(F)_{Xavier}=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability of success of Yvonne, [tex]P(S)_{Yvonne}=\frac{1}{2}[/tex]
Probability of failure of Yvonne, [tex]P(F)_{Yvonne}=1-\frac{1}{2}=\frac{1}{2}[/tex]
Probability of success of Zelda, [tex]P(S)_{Zelda}=\frac{5}{8}[/tex]
Probability of failure of Zelda, [tex]P(F)_{Zelda}=1-\frac{5}{8}=\frac{3}{8}[/tex]
We need to calculate:
The probability that Xavier and Yvonne can solve the problem but Zelda cannot, we use:
[tex]P(S)_{Xavier}\times P(S)_{Yvonne}\times P(F)_{Zelda}=\frac{1}{4}\times \frac{1}{2}\times \frac{3}{8}=\frac{3}{64}[/tex]
Hence, the probability that Xavier and Yvonne can solve a problem but Zelda cannot is [tex]\frac{3}{64}[/tex]
