Problem

35. A bag contains three chocolate candies and two vanilla candies. What is the probability of drawing all three chocolate candies in three consecutive draws (without replacing them each time)?

Answer

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Answer

Final Answer: The probability of drawing all three chocolate candies in three consecutive draws (without replacing them each time) is \(\boxed{0.1}\).

Steps

Step 1 :The problem is asking for the probability of drawing all three chocolate candies in three consecutive draws from a bag that contains three chocolate candies and two vanilla candies, without replacing them each time.

Step 2 :The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.

Step 3 :In this case, the event is drawing all three chocolate candies in three consecutive draws. There is only one way this can happen, so the number of ways the event can occur is \(1\).

Step 4 :The total number of outcomes is the total number of ways we can draw three candies from a bag of five. This is calculated as \(5 \times 4 \times 3 = 60\). However, since the order of drawing does not matter, we need to divide this by the number of ways to arrange three candies, which is \(3 \times 2 \times 1 = 6\). So the total number of outcomes is \(\frac{60}{6} = 10\).

Step 5 :Therefore, the probability is calculated as \(\frac{1}{10} = 0.1\).

Step 6 :Final Answer: The probability of drawing all three chocolate candies in three consecutive draws (without replacing them each time) is \(\boxed{0.1}\).

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