six girls and four boys have entered the science fair. first, second, and third place awards are to be given…

Explanation:

Step1: Calculate probability of a girl winning first - place

There are 6 girls and 4 boys, so a total of 10 people. The probability that a girl wins first - place is $\frac{6}{10}$ since there are 6 favorable outcomes (girls) out of 10 total outcomes.

Step2: Calculate probability of a boy winning second - place

After a girl wins first - place, there are 9 people left, and 4 of them are boys. So the probability that a boy wins second - place is $\frac{4}{9}$.

Step3: Calculate probability of a boy winning third - place

After a girl wins first - place and a boy wins second - place, there are 8 people left, and 3 of them are boys. So the probability that a boy wins third - place is $\frac{3}{8}$.

Step4: Calculate the combined probability

We use the multiplication rule for independent events (the order of selection matters here). The combined probability $P=\frac{6}{10}\times\frac{4}{9}\times\frac{3}{8}=\frac{72}{720} = 0.1$.

Answer:

10%