Questions: Given the joint probability table above what is P[Not A B]? .50 .25 .75 .56

Given the joint probability table, calculate \( \mathrm{P}[\operatorname{Not} \mathrm{A} \mid \mathrm{B}] \).

Identify the relevant probabilities from the table.

From the table:

• \( \mathrm{P}(B) = 0.20 \)
• \( \mathrm{P}(\operatorname{Not} A \cap B) = 0.05 \)

The probability \( \mathrm{P}[\operatorname{Not} \mathrm{A} \mid \mathrm{B}] \) is calculated as: \[ \mathrm{P}[\operatorname{Not} \mathrm{A} \mid \mathrm{B}] = \frac{\mathrm{P}(\operatorname{Not} A \cap B)}{\mathrm{P}(B)} = \frac{0.05}{0.20} = 0.25 \] \[ \boxed{0.25} \]

The probability \( \mathrm{P}[\operatorname{Not} \mathrm{A} \mid \mathrm{B}] \) is \boxed{0.25}.