Final answer:
The probability that the boys and girls will be in alternate positions is 1/35.
Step-by-step explanation:
To find the probability that the boys and girls will be in alternate positions, we need to calculate the total number of possible arrangements where the boys and girls are alternated and divide it by the total number of possible arrangements.
First, we calculate the total number of possible arrangements. There are 7 positions in the queue, and there are 4 boys and 3 girls. So, the total number of possible arrangements is 7!
Next, we calculate the number of arrangements where the boys and girls are alternated. We can think of it as arranging the boys and girls separately. The number of arrangements of the boys is 4! and the number of arrangements of the girls is 3!. So, the number of arrangements where the boys and girls are alternated is 4! * 3!.
Finally, the probability is the number of arrangements where the boys and girls are alternated divided by the total number of possible arrangements. So the probability is (4! * 3!) / 7!.
Simplifying the expression, we get the probability to be 1/35.