A candy store grab bag contains 10 pieces of sour candy, 12 pieces of chocolate candy, and 6 pieces of sweet candy. If you select 1 piece of candy, replace it, and then select another piece, what is the probability that the first piece of candy taken out is a sour candy and the second piece of candy taken out is not a sour candy?100%23%92%29%
Question
A candy store grab bag contains 10 pieces of sour candy, 12 pieces of chocolate candy, and 6 pieces of sweet candy. If you select 1 piece of candy, replace it, and then select another piece, what is the probability that the first piece of candy taken out is a sour candy and the second piece of candy taken out is not a sour candy?100%23%92%29%
Solution
To solve this problem, we need to calculate two separate probabilities and then multiply them together.
- The probability that the first piece of candy taken out is a sour candy.
- The probability that the second piece of candy taken out is not a sour candy.
Step 1: Calculate the total number of candies in the bag. The total number of candies is 10 (sour) + 12 (chocolate) + 6 (sweet) = 28 candies.
Step 2: Calculate the probability of drawing a sour candy first. The probability of drawing a sour candy first is the number of sour candies divided by the total number of candies. So, 10 (sour candies) / 28 (total candies) = 0.357 or 35.7%.
Step 3: Since the candy is replaced after the first draw, the total number of candies remains the same for the second draw. The probability of not drawing a sour candy is calculated by dividing the number of candies that are not sour by the total number of candies. So, 18 (chocolate and sweet candies) / 28 (total candies) = 0.643 or 64.3%.
Step 4: The probability that the first candy drawn is sour and the second candy drawn is not sour is calculated by multiplying the two probabilities calculated in steps 2 and 3. So, 0.357 * 0.643 = 0.229 or 22.9%.
So, the probability that the first piece of candy taken out is a sour candy and the second piece of candy taken out is not a sour candy is approximately 23%.
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