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 = }(5)/(11)\text{ }*\text{ }(4)/(10)\text{ =}(2)/(11)\text{ }`
`\begin{gathered} \text{Probability of selection two boys} \\ \text{Probability of selection two girls =}(6)/(9)\text{ }*(5)/(8)\text{ = }(15)/(36)\text{ } \end{gathered}`

Next

Final answer

`\begin{gathered} =\text{ }(2)/(11)\text{ }*\text{ }(5)/(36)\text{ } \\ =\text{ }(5)/(198) \end{gathered}`

= 0.025253