3 students are selected from a class that has 10 boys and 5 girls. What is the probability that 1 boy and 2 girls are selected?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The class has 10 boys and 5 girls. In all there are 15 students.

The number of ways in which 3 students can be selected is 3C15

=> 15! / 3!*12!

=> 455

The number of ways that those selected are 1 boy and 2 girls is 2C5*1C10

=> 5!/2!*3! * 10!/1!*9!

=> 100

The probability is the ratio of the desired events to the total number of events possible.

This is 100/455

The probability that of the 3 students selected 1 is a boy and 2 are girls is 100/455

bhalachandra's profile pic

bhalachandra | College Teacher | (Level 1) eNoter

Posted on

The  class  has  15  students of which 10 are boys and 5 are girls.   Three  students  are  selected  (at  random).

We further assume that  the selection is  made by SRSWOR.

Total number of ways in which 3 students can be selected from 15 students is 15 C 3 =  (15*14*13)/ 3!  = 455.

Again, 1 boy can be selected from 10 boys in 10C1  =  10  ways.  Also,  2 girls can be selected from 5 girls in 5C2  =  10  ways.  By multiplication principle,  the combined event  can occur in 10*10 = 100  ways.

By  using classical definition of probability,  the required probability  is 100 / 455 =  20 / 91.

 

 

 

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