Question

Mrs. Janssen has a class of 10 students. In her class, there are 4 boys and 6 girls. Mrs. Janssen chooses two students from her class randomly.
What is the probability that she did NOT choose a boy either time?

Answer 1

Probabilities are used to determine the chance of events

The probability that she did NOT choose a boy either time is 1/3

The given parameters are given as:

$\mathbf{n = 10}$ --- total number of students

$\mathbf{Boys = 4}$ --- total number of boys

$\mathbf{Girls = 6}$ ---- total number of girls

If she did not choose a boy in either selection, then it means that both selections are girls.

So, the probability is calculated using:

$\mathbf{P = P(Girl) \times P(Girl)}$

The selection is without replacement.

So, we have:

$\mathbf{P = \frac{Girl}{n} \times \frac{Girl-1}{n-1}}$

Substitute known values

$\mathbf{P = \frac{6}{10} \times \frac{6-1}{10-1}}$

$\mathbf{P = \frac{6}{10} \times \frac{5}{9}}$

Simplify

$\mathbf{P = \frac{1}{3}}$

Hence, the probability is 1/3

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