Question

a small class has 10 students 5 are girls5 are boysThe teacher is going to choose 2 students at random. what is the probability that the first student is a boy, and the second a girl?write as a fraction in the simplest form

Answer 1

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,

`^(10)C_1\text{ }`

Number of ways in which the second student is selected is given as,

`^9C_1`

Total number of ways in which both the students are selected is given as,

`\text{Total number of ways = }^(10)C_1\text{ }*\text{ }^9C_1`

Number of ways in which a girl is selected is given as,

`^6C_1`

Number of ways in which a girl is selected is given as,

`^5C_1`

Number of ways in which a boy is selected is given as,

`^5C_1`

The probability in which in first student selected is a boy and the second student selected is a girl is ,

`\begin{gathered} \text{Required probability = }\frac{^5C_1\text{ }*\text{ }^5C_1}{^(10)C_1\text{ }*\text{ }^9C_1} \\ \text{Required probability = }\frac{5\text{ }*\text{ 5}}{10\text{ }*9} \\ \text{Required probability = }(25)/(90)\text{ = }(5)/(18) \\ \text{Required probability = 0.28} \end{gathered}`

Thus the required probability is 0.28 .