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