Could you ever add enough red marbles to a container so that the probability of getting a red marble would be 1? Explain.
Hello, jthomp18!
Could you ever add enough red marbles to a container
so that the probability of getting a red marble would be 1? .Explain.
Think about it . . .
"P(red) = 1" means we are 100% certain that we will draw a red marble.
But as long as there is, say, one blue marble in the container,
. . the probability of drawing a red marble will never be 1.
P(blue) can be small: $\displaystyle \tfrac{1}{1000}$
. . It can be very small: $\displaystyle \tfrac{1}{1,000,000,000}$
. . . . It can be extremely small: $\displaystyle \tfrac{1}{10^{100}}$
But there is always the chance that the blue ball will be drawn.
On the page to which you gave the link, there is a "Probability" link on the left. The instructions there say: "For each of the following problems, consider how you would pose the same problem to your students. Would the wording need to change?" Maybe that question was supposed to be changed. I could give several other scenarios where the probability of drawing a red marble is 1.
(1) When the container initially has only red marbles (empty container is a special case of this).
(2) When the marbles are not mixed so that the added red marbles are on top.
(3) When the container initially has finitely many green marbles and one adds infinitely many red ones.
Thank you Soroban. I think that is what my professor will be looking for.
MHF Contributor...thank you for your answer as well. It really helped me think through the question and also see other scenarios.
You both are very kind and helpful.