Quantitative Literacy Practice Exam

When drawing from a bag of 15 balls (5 red, 5 blue, 5 green) without replacement, how do you calculate the probability of drawing two blue balls?

1. 5/15 x 4/14

2. 5/15 x 5/14

3. 5/15 x 3/14

4. 5/15 x 1/14

The correct answer is: 5/15 x 4/14

To determine the probability of drawing two blue balls from a bag containing 15 balls (5 red, 5 blue, 5 green) without replacement, it is essential to understand the mechanics of how probabilities work in this scenario. The first ball you draw is blue, so the probability of that happening is the number of blue balls divided by the total number of balls in the bag. There are 5 blue balls out of 15 total balls, which gives a probability of 5/15 for the first draw. Once the first blue ball has been drawn, there are now 14 balls remaining in the bag (4 blue, 5 red, and 5 green). Therefore, the probability of drawing a second blue ball is the number of remaining blue balls divided by the total number of remaining balls. After removing one blue ball, there are now 4 blue balls left and 14 total balls in the bag. This gives a probability of 4/14 for the second draw. To find the joint probability of both events happening (drawing the first blue and then the second blue), you multiply the probabilities of the two independent events: (5/15) * (4/14) This is why the correct choice involves multiplying 5