This unfortunate event happened to me when my two children were little. Each of them had a friend over for lunch. After lunch, we had popsicles for dessert. There were 9 popsicles in the freezer & 3 flavors: 3 grape, 3 cherry, & 3 orange. What is the probability that each child will get the popsicle that child wants.
Well, let's take a look at this delicious popsicle predicament. With 9 popsicles in total and 3 flavors each, we have a 1 in 3 chance of picking the desired flavor for each child. So the probability of the first child getting the desired popsicle is 1/3.
Now, assuming that each child chooses a popsicle without replacement (meaning they can't put it back once it's taken), the probability for the second child would be 2/8, since there would be two desired flavors left out of the remaining 8 popsicles.
Finally, for the last child, the probability would be 1/7, as there would only be one desired flavor left out of the remaining 7 popsicles.
To calculate the overall probability, we just multiply these individual probabilities together: (1/3) * (2/8) * (1/7) = 2/168 ≈ 0.012.
So, to answer your question, the probability that each child will get the popsicle they want is approximately 0.012, or in simpler terms, not very likely. But hey, sometimes life throws us curveballs, or in this case, pop-skulls!
To find the probability that each child will get the popsicle they want, we need to analyze the possible outcomes.
Let's consider the different scenarios:
Scenario 1: The first child picks a popsicle and gets the one they want.
Possible outcomes: 3 (One grape, cherry, or orange)
Scenario 2: The first child picks a popsicle and doesn't get the one they want, then the second child picks a popsicle and gets the one they want.
Possible outcomes: 6 (Two popsicles different from their desired one, followed by any of the remaining 2 desired popsicles)
Scenario 3: The first child picks a popsicle and doesn't get the one they want, then the second child picks a popsicle and also doesn't get the one they want, and finally, the third child picks a popsicle and gets the one they want.
Possible outcomes: 3 (Two popsicles different from their desired ones, followed by their desired popsicle)
Hence, the total number of favorable outcomes is 3 (scenario 1).
The total number of possible outcomes is 9 (since there are 9 popsicles in total).
Therefore, the probability that each child will get the popsicle they want is 3/9, which simplifies to 1/3 or approximately 0.3333.
To determine the probability that each child will get the popsicle they want, we first need to understand the possible outcomes.
In this scenario, each child has a choice between three flavors: grape, cherry, and orange. Since there are no restrictions, the first child can choose any one of the nine popsicles available. After the first child makes their choice, there will be eight popsicles left, two of each flavor.
The second child also has a choice of three flavors, but since the first child has already taken one of each, there will be only two popsicles left for each flavor. Therefore, the probability of the second child getting the desired popsicle will depend on what flavor the first child selected.
Let's consider the different scenarios:
1. The first child chooses grape: In this case, there are two grape, two cherry, and three orange popsicles left. Since the second child wants a grape popsicle, there are two grape popsicles out of seven remaining options for the second child, resulting in a probability of 2/7.
2. The first child chooses cherry: Similar to the first scenario, there are two cherry, two grape, and three orange popsicles left. The second child wants a cherry popsicle, so there are two cherry popsicles out of seven remaining options, yielding a probability of 2/7.
3. The first child chooses orange: Again, there are two orange, two grape, and two cherry popsicles left. Since the second child also wants an orange popsicle, there are two orange popsicles out of six remaining options, leading to a probability of 2/6, which simplifies to 1/3.
Now, we need to consider both children's choices, so we multiply the probabilities together. Since there are three equally likely scenarios (the first child chooses grape, cherry, or orange), we can add the probabilities for each scenario and divide by three to obtain the overall probability.
Probability = [(2/7) + (2/7) + (1/3)] / 3 = (4/7 + 1/3) / 3 = (24/21 + 7/21) / 3 = 31/21 / 3 = 31/63 ≈ 0.492
Therefore, the probability that each child will get the popsicle they want is approximately 0.492 or 49.2%.