Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram. $P(A)=0.19, P(B)=0.71$ and $P(A$ and $B)=0.10$. \[ P(\operatorname{not} B \mid \operatorname{not} A)= \]

Step 1 ：Given the probabilities: \(P(A)=0.19\), \(P(B)=0.71\) and \(P(A \text{ and } B)=0.10\)

Step 2 ：First, we need to find the probabilities of not A and not B. These are the complements of A and B, respectively. So, \(P(\text{not } A) = 1 - P(A) = 1 - 0.19 = 0.81\) and \(P(\text{not } B) = 1 - P(B) = 1 - 0.71 = 0.29\)

Step 3 ：Next, we need to find the probability of not A and not B. This is the complement of A or B, so \(P(\text{not } A \text{ and not } B) = 1 - P(A \text{ or } B) = 1 - (P(A) + P(B) - P(A \text{ and } B)) = 1 - (0.19 + 0.71 - 0.10) = 0.20\)

Step 4 ：Finally, we can use the formula for conditional probability to find the answer. The formula is \(P(B|A) = \frac{P(A \text{ and } B)}{P(A)}\). Substituting in our values, we get \(P(\text{not } B|\text{not } A) = \frac{P(\text{not } A \text{ and not } B)}{P(\text{not } A)} = \frac{0.20}{0.81} = 0.247\)

Step 5 ：So, the conditional probability of not B given not A is approximately \(\boxed{0.247}\)