Question

six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the probability that a girl wins the first place award while boys will receive the second and third place awards? express your answer as a percent. 10% 14% 18% 22%

Explanation:

Step1: Calculate total participants

Total students = 6 girls + 4 boys = 10.

Step2: Probability of girl first

Probability girl wins first: $\frac{6}{10}$.

Step3: Probability of boy second

After a girl wins first, 9 left, 4 boys. Probability: $\frac{4}{9}$.

Step4: Probability of boy third

After girl first and boy second, 8 left, 3 boys. Probability: $\frac{3}{8}$.

Step5: Multiply probabilities

Total probability = $\frac{6}{10} \times \frac{4}{9} \times \frac{3}{8}$ = $\frac{6\times4\times3}{10\times9\times8}$ = $\frac{72}{720}$ = 0.1 = 10%.

Answer:

10%