Question

You select a marble without looking and then put it back. If you do this 6 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?

Answer 1

To predict the number of times you will pick a marble that is not orange after selecting a marble 6 times, we first need to know the probability of picking a marble that is not orange.

Let's assume the probability of picking an orange marble is \( P(\text{orange}) \) and the probability of picking a marble that is not orange is \( P(\text{not orange}) \).

The two probabilities are related as follows:
\[
P(\text{not orange}) = 1 - P(\text{orange}).
\]

If we denote \( n \) as the total number of marbles, and \( k \) as the number of orange marbles, we can express the probabilities as:
\[
P(\text{orange}) = \frac{k}{n},
\]
\[
P(\text{not orange}) = 1 - \frac{k}{n} = \frac{n - k}{n}.
\]

Assuming that you have an equal number of orange and non-orange marbles, or if you're unaware of the exact proportions, we might suggest a \( P(\text{not orange}) \) of about \( 0.5 \).

Given that you're drawing marbles 6 times, the expected (or best prediction) number of times you would draw a marble that is not orange can be calculated as:
\[
\text{Expected number of not orange marbles} = 6 \times P(\text{not orange}).
\]

If \( P(\text{not orange}) = 0.5 \):
\[
\text{Expected number of not orange marbles} = 6 \times 0.5 = 3.
\]

If the proportion is anything else, just plug in the actual value of \( P(\text{not orange}) \) into the formula. Without specific information on the number of orange versus non-orange marbles, a fair estimate for the number of times you will pick a marble that is not orange would be:

\[
\boxed{3}.
\]