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 girl winning first

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

Step2: Calculate probability of boy winning second

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

Step3: Calculate probability of boy winning third

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

Step4: Calculate combined probability

We multiply the probabilities of each event: $\frac{6}{10}\times\frac{4}{9}\times\frac{3}{8}=\frac{72}{720} = 0.1$.

Answer:

10%