Mathematics

Question


A small class has
9
students,
5
of whom are girls and
4
of whom are boys. The teacher is going to choose two of the students at random. What is the probability that the first student chosen will be a girl and the second will be a boy? Write your answer as a fraction in simplest form.

2 Answer

  • 1 out of 9 because the teacher will either choose one girl or boy
  • Answer:

    [tex]\frac{5}{18}[/tex] is the probability that the first student chosen will be a girl and the second will be a boy.    

    Step-by-step explanation:

    we are given the following information in the question:

    Total number of students in a class = 9

    Total number of girls in a class = 5

    Total number of boys in a class = 4

    We have to find the probability that the first student chosen will be a girl and the second will be a boy.

    Formula:

    [tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]

    [tex]\text{P(first student chosen will be a girl and the second will be a boy)}=\\\text{P(first student chosen will be a girl)}\times \text{P(second student chosen will be a will be a boy)}[/tex]

    Working:

    [tex]\text{P(first student chosen will be a girl)} = \displaystyle\frac{5}{9}\\\\\text{P(second student chosen will be a boy)} = \displaystyle\frac{4}{8}\\\\[/tex]

    [tex]\text{P(first student chosen will be a girl and the second will be a boy)}= \displaystyle\frac{5}{9}\times \frac{4}{8}\\\\\frac{20}{72} = \frac{5}{18}[/tex]

    Hence, [tex]\frac{5}{18}[/tex] is the probability that the first student chosen will be a girl and the second will be a boy.

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