Respuesta :
Total number of students = 10
Total number of girls = 5
Total number of boys = 5
Number of ways in which the first student is selected is given as,
[tex]^{10}C_1\text{ }[/tex]Number of ways in which the second student is selected is given as,
[tex]^9C_1[/tex]Total number of ways in which both the students are selected is given as,
[tex]\text{Total number of ways = }^{10}C_1\text{ }\times\text{ }^9C_1[/tex]Number of ways in which a girl is selected is given as,
[tex]^6C_1[/tex]Number of ways in which a girl is selected is given as,
[tex]^5C_1[/tex]Number of ways in which a boy is selected is given as,
[tex]^5C_1[/tex]The probability in which in first student selected is a boy and the second student selected is a girl is ,
[tex]\begin{gathered} \text{Required probability = }\frac{^5C_1\text{ }\times\text{ }^5C_1}{^{10}C_1\text{ }\times\text{ }^9C_1} \\ \text{Required probability = }\frac{5\text{ }\times\text{ 5}}{10\text{ }\times9} \\ \text{Required probability = }\frac{25}{90}\text{ = }\frac{5}{18} \\ \text{Required probability = 0.28} \end{gathered}[/tex]Thus the required probability is 0.28 .
