natalie has a bag that contains eight marbles. she draws out a marble, record its color, and puts it back. if natalie repeats this eight times and does not record any red marbles, can she concludes that there are not any red marbles in the bag? Explain
How does she know that she wasn't picking the same marble each time?
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A container has 3 blue pens, 4 red pens and 6 yellow pens. In how many ways can you get 4 pens if you need to get at least 1 red pen?
To determine whether Natalie can conclude that there are no red marbles in the bag, we need to consider the concept of inference and probability.
Given that Natalie has a bag with eight marbles and she randomly draws a marble, records its color, and puts it back, this process is known as sampling with replacement. In this case, each draw is independent of the others, meaning the probability of drawing a red marble remains the same across all draws.
If Natalie draws a marble eight times without recording any red marbles, it does imply that she has not encountered a red marble in those eight draws. However, she cannot definitively conclude that there are no red marbles in the bag. The reason for this lies in the concept of probability.
Probability is the measure of the likelihood of an event occurring. In this case, the probability of drawing a red marble can only be estimated based on the sample observed. Since Natalie has only drawn eight marbles, the sample size is relatively small, and it may not provide a representative picture of the bag's contents as a whole.
To draw more reliable conclusions, Natalie would need to continue drawing and recording marbles over a larger number of trials. The more she repeats the process, the more accurate her estimation of the probability of drawing a red marble becomes.
In summary, while Natalie's observations indicate that she has not encountered any red marbles in the eight draws she recorded, she cannot definitively conclude that there are no red marbles in the bag. To make a more accurate inference, she would need to continue drawing marbles and gather more data.