Sara has 5 blue bows and 7 white bows in a bag for her fellow cheerleaders to wear in their hair for each game. The bows are
pulled out randomly by the team. Determine if the following is an
Independent or a Dependent event. Then find the probability.

1.) Sara pulls out a blue bow and her teammate pulls out a white bow.

If the first bow Sara pulls out isn't put back, then the two events are dependent. This is because the probability of pulling a white bow changes depending on what Sara pulls out.

If Sara pulls out a blue bow, then the teammate's chances of pulling a white bow are 7/11 because there are 7 white bows out of 4+7 = 11 left over (or you could compute 5+7-1 = 11).
Or if Sara pulls out a white bow, then the chances of a teammate pulling out another white bow is 6/11 instead of 7/11. The probability has changed.

So again, it all depends on what Sara does because she goes first. This is of course not the case if Sara puts the bow back. If she put it back, then the chances of the teammate pulling the white bow is 7/12

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To find the overall probability of Sara selecting a blue bow and not putting it back, followed by a teammate getting a white bow, we multiply the fractions 5/12 and 7/11 to get (5/12)*(7/11) = 35/132

For more info, search out conditional probability.