Question

A swim team consists of 6 boys and 5 girls. A relay team of 4 swimmers is chosen at random from the team members. What is the probability that 2 boys are selected forthe relay team given that the first 2 selections were girls? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth

Answer 1

Concept

$\text{Probability of any event = }\frac{No\text{ of required outcome}}{No\text{ of sample safe}}$

Next,

Number of sample space = 11

Let the probability of selecting boys = P(B) and the probability of selecting girls = P(G)

$\text{Probability of selecting 2 girls = }\frac{5}{11}\text{ }\times\text{ }\frac{4}{10}\text{ =}\frac{2}{11}\text{ }$$\begin{gathered} \text{Probability of selection two boys} \\ \text{Probability of selection two girls =}\frac{6}{9}\text{ }\times\frac{5}{8}\text{ = }\frac{15}{36}\text{ } \end{gathered}$

Next

Final answer

$\begin{gathered} =\text{ }\frac{2}{11}\text{ }\times\text{ }\frac{5}{36}\text{ } \\ =\text{ }\frac{5}{198} \end{gathered}$

= 0.025253