A box of cookies contains 4 chocolate and 6 butter cookies. Miguel randomly selects a cookie and eats it. Then he randomly selects another cookie and eats it. Are the probabilities for the flavor of the second cookie that Miguel selects independent of his first selection? Explain. The probabilities for the second cookie selection are independent of the first selection. The cookies are replaced after selecting them. The probabilities for the second cookie selection are dependent on the first selection. The probability of selecting a chocolate cookie second is the same as selecting a butter cookie. The probabilities for the second cookie selection are dependent on the first selection. The probability of a chocolate cookie being selected second is dependent on whether a chocolate or butter cookie was selected first. The probabilities for the second cookie selection

The probability of the flavor of the second cookie is always going to be dependent on the first one eaten.

Step-by-step explanation:

Since the number of the type of cookies left depends on the first cookie taken out.

This is better explained with an example:

Probability Miguel eats a chocolate cookie is 4/10. The probability he eats a chocolate or butter cookie after that is 3/9 and 6/9 respectively. This is because there are now only 3 chocolate cookies left and still 6 butter cookies left. In another case, Miguel gets a butter cookie on the first try with the probability of 6/10. The cookies left are now 4 chocolate and 5 butter cookies. The probability of the next cookie being chocolate or butter is now 4/9 and 5/9 respectively.

The two scenarios give us different probabilities for the second cookie. This means that the probability of the second cookie depends on the first cookie eaten.