A bag of chocolate candies has the following colors: 5 yellow, 7 green, 8 red, 5 orange, and 4 brown. What is the probability of getting two of the same color when pouring two out of the bag?
a. Describe a simulation that could be used to answer the preceding question.
could be
1. YY --->(5/29)(4/28) = 20/812
2. GG ---> (7/29)(6/28) = 42/812
...
5. BB ---> 4/29)(3/28) = 12/812)
Add them up
(20 + 42 + .. + 12)812
= ....
To simulate the event of pouring two candies out of the bag, you could follow these steps:
1. Assign a specific number to each color of candy - for example, 1 for yellow, 2 for green, 3 for red, 4 for orange, and 5 for brown.
2. Create an array or list representing the candies in the bag, where each element corresponds to a candy color and its quantity. Using the information given, the bag's representation would be: [5 yellow, 7 green, 8 red, 5 orange, 4 brown].
3. Randomly select two candies from the bag. You can do this by generating two random numbers between 1 and the total number of candies in the bag.
4. Check if the two selected candies are of the same color. If they are, count it as a favorable outcome.
5. Repeat the previous steps a large number of times (e.g., 10,000) to obtain a sufficient sample size.
6. Calculate the probability of getting two candies of the same color by dividing the number of favorable outcomes (same color candies) by the total number of simulations performed.
By following this simulation approach, you can estimate the probability of pouring two candies of the same color from the bag.