The probability that a family prefers tea of brand A is 0.3. Find the probability that the tenth family in a survey is found to be fifth one, who prefer tea of brand A.

There were 9 families before tenth and since tenth family must be fifth who prefer brand A then among these 9 families there must be four families who prefer brand A.

Let X be a random variable representing the number of families before tenth who prefer brand A, then X~Bin(9, 0.3)

$P(X=4)={9 \choose 4}*0.3^4*0.7^5\approx0.17$

The probability that the tenth family prefers brand A is 0.3, so the sought probability is 0.17*0.3=0.051