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Ln a Class, There Are 15 Boys and 10 Girls. Three Students Are Selected at Random. the Probability that 1 Girl and 2 Boys Are Selected, is - Mathematics

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MCQ

ln a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is

Options

  • `21/46`

  • `25/117`

  • `1/50`

  • `3/25`

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Solution

`21/46`

Explanation:
Let S be the sample space and E be the event of selected 1 girl and 2 boys.
Then, n(S) = Number of ways selecting 3 students out of 25.

= `""^25C_3=((25xx24xx23))/((3xx2xx1))`

= 2300

n(E) = `(""^10C_1xx""^15C_2)`

= `[10xx((15xx14))/((2xx1))]= 1050`

∴ P E = `(n(E))/(n(S))=1050/2300=21/46`

Concept: Probability (Entrance Exam)
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