Question

A box of jerseys for a pick up game of basketball contains 8 extra large jerseys, 6 large jerseys and 5 medium jerseys. if you are first to the box and grab 2 jerseys, what is the probability that you randomly grad 2 large jerseys? express your answer as a fraction

Answer 1

The box of jerseys contains :

8 extra-large jerseys

6 large jerseys

5 medium jerseys

Total of jerseys in the box = 19 jerseys

You are the first, therefore the box has all the jerseys.

Now, you grab 2 jerseys.

The odds that the first jersey is extra large is given by the formula:

$p=\frac{\#\text{ of large jerseys}}{\text{Total of jerseys}}$

So the probability for the first jersey is:

$p=\frac{6}{19}$

For the second jersey, we already take out one jersey from the box:

Therefore, now the total of jerseys is 18 in the box.

We assume that the jersey one is large, therefore, now we have 5 large jerseys.

Use the same probability formula to find the second jersey:

$p2=\frac{5}{18}$

Finally, to find the probability that you randomly grad 2 large jerseys, you just need to multiply both probabilities:

$p\cdot p2=\frac{6}{19}\cdot\frac{5}{18}=\frac{6\cdot5}{19\cdot18}$$p\cdot p2\text{ =}\frac{5}{57}$