A bag contains 3 blue marbles and 4 red marbles. What is the probability that three randomly drawn marbles without replacement will all be red?

Answer 1

The probability of drawing 3 red marbles in a row from a bag of 3 blue and 4 red marbles without replacement is right at about 0.11 or about 11 in 100, if you want odds.

Remember that probability is a pure number between zero (no chance - it's impossible) and 1 (it will happen - it's a certainty). A probability of 0.5 is a 50-50 shot, like a coin toss. We good? Let's move on.

We have 7 marbles, and there is a 4 in 7 shot of getting a red marble in the first draw. There is a 3 in 6 shot the next draw since now we only have 6 marbles total (NO replacement) and only 3 red ones (we already drew a red one out). Similarly, there is a 2 in 5 shot of getting a third red one if the first two are red. The probability of the first action (getting a red marble on the first draw) is 4/7 or a probability of about 0.5714. Second draw, it's 3/6 or a probability of 0.5. Last, it's 2/5 or a probability of 0.40. To find the intersection of these probabilities, we just multiply them all together, and we'll get right at about 0.011 for a probability.