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 the total number of participants

There are \(6\) girls and \(4\) boys, so the total number of participants \(n = 6 + 4=10\)

Step2: Calculate the probability of a girl winning first place

The probability that a girl wins first place \(P_1=\frac{6}{10}\)
After a girl wins first place, there are \(9\) participants left, with \(4\) boys.

Step3: Calculate the probability of a boy winning second place

The probability that a boy wins second place \(P_2=\frac{4}{9}\)
After a girl wins first - place and a boy wins second - place, there are \(8\) participants left, with \(3\) boys.

Step4: Calculate the probability of a boy winning third place

The probability that a boy wins third place \(P_3=\frac{3}{8}\)

Step5: Calculate the combined probability

Since these are independent events (the result of one award does not affect the probability of the next award in terms of the basic probability formula for sequential non - replacement events), the combined probability \(P = P_1\times P_2\times P_3\)

$$
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Step6: Convert to percentage

To convert the decimal to a percentage, we multiply by \(100\). So \(P = 0.1\times100\%=10\%\)

Answer:

10%