Probability

Question

Mr. Wilson's second grade class has 22 students, 12 girls and 10 boys. Two students must be selected at random to be in the fall play. What is the probability that no boys will be chosen?

Answer 1

Hi Daniella,

The probability that no boys are chosen is equal to:

 

  the probability that the first student selected is not a boy (so, is a girl)

     times

  the probability that the second student selected is not a boy.

 

These two probabilities are:

first pick, chance to get a girl:

    12 girls

    --------         =   6/11

    22 students

 

the second pick has one less girl and student (the one from the first pick)

so the probability this pick is a girl is:

   11 girls

   ---------        =  11/21

   21 students

 

multiplying these we get:

 

P = (6/11) * (11/21) 

  = 6/21

  = 2/7   or about 0.286  or as a percent:  28.6%