Problem

There are 32 chocolates in a box, all identically shaped. There 12 are filled with nuts, 11 with caramel, and 9 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
$9 / 16$ or 0.5625
$81 / 1024$ or 0.0791
$9 / 124$ or 0.0726

Answer

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Answer

Final Answer: The probability of selecting 2 solid chocolates in a row is \(\boxed{0.0726}\) or \(\boxed{7.26\%}\).

Steps

Step 1 :The problem is asking for the probability of selecting two solid chocolates in a row. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.

Step 2 :In this case, the total number of outcomes is the total number of chocolates, which is 32. The number of ways to select a solid chocolate is 9 (since there are 9 solid chocolates).

Step 3 :So, the probability of selecting a solid chocolate on the first pick is \(\frac{9}{32}\).

Step 4 :After eating one solid chocolate, there are now 31 chocolates left, 8 of which are solid. So, the probability of selecting a solid chocolate on the second pick is \(\frac{8}{31}\).

Step 5 :The probability of both events happening (i.e., selecting a solid chocolate on the first pick AND selecting a solid chocolate on the second pick) is the product of the probabilities of each event.

Step 6 :Final Answer: The probability of selecting 2 solid chocolates in a row is \(\boxed{0.0726}\) or \(\boxed{7.26\%}\).

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