Given $P(A)=0.74,P(B)=0.85$ and $P(A\mid B)=0.84$, find the value 0 $P(A$ and $B)$, rounding to the nearest thousandth, if necessary.

Step 1 ：Given $P(A)=0.74$, $P(B)=0.85$ and $P(A\mid B)=0.84$, find the value of $P(A\text{ and }B)$, rounding to the nearest thousandth, if necessary.

Step 2 ：We need to find the probability of $P(A\text{ and }B)$, which can be calculated using the conditional probability formula: $P(A\mid B)=\frac{P(A\text{ and }B)}{P(B)}$. We have the values of $P(A\mid B)$, $P(A)$, and $P(B)$, so we can solve for $P(A\text{ and }B)$.

Step 3 ：$P(A\mid B)=0.84$

Step 4 ：$P(A)=0.74$

Step 5 ：$P(B)=0.85$

Step 6 ：Using the conditional probability formula, we get:

Step 7 ：$0.84=\frac{P(A\text{ and }B)}{0.85}$

Step 8 ：Solving for $P(A\text{ and }B)$, we get:

Step 9 ：$P(A\text{ and }B)=0.84\times 0.85$

Step 10 ：$P(A\text{ and }B)=0.714$

Step 11 ：$\boxed{{\displaystyle 0.714}}$