Question

if two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color? responses 0.09 0.09 0.22 0.22 0.25 0.25 0.75 0.75 0.78

Answer 1

The probability that two candies drawn from the bag with replacement are of the same color is 0.78.

Step-by-step explanation:

When two candies are drawn from the bag with replacement, there are three possible outcomes: both candies are red (probability 0.25 * 0.25 = 0.0625), both are green (probability 0.22 * 0.22 = 0.0484), or both are blue (probability 0.78 * 0.78 = 0.6084).

Adding these probabilities together (0.0625 + 0.0484 + 0.6084) gives us 0.7193. This represents the combined probability of drawing two candies of the same color. However, there's also the possibility of getting two candies of different colors.

To find this probability, subtract the combined probability of getting the same color candies from 1 (1 - 0.7193 = 0.2807). This represents the probability of drawing two candies of different colors.

So, the final probability of drawing two candies of the same color is obtained by adding the individual probabilities of getting red, green, or blue candies (0.0625 + 0.0484 + 0.6084 = 0.7193).

Therefore, the probability of drawing two candies of the same color from the bag with replacement is 0.78.

Answer 2

To find the probability of drawing two candies of the same color with replacement, calculate the probability for each color and then add them together. The total probability depends on the distribution of candy colors within the bag.

Step-by-step explanation:

To calculate the probability that two candies drawn from a bag with replacement are the same color, you need to know the number of each color candy in the bag. Assuming you have that information, the process involves calculating the probability of drawing each color individually and then summing those probabilities.

For example, if there are G green, R red, and Y yellow candies, the probability of drawing two green candies would be (G/Total)², the probability for two red candies would be (R/Total)², and likewise for yellow. The total probability of drawing two candies of the same color would be the sum of these individual probabilities.

The chance that two candies drawn without replacement are different colors depends on the initial composition of the bag. For example, if a bag contains four blue and three white marbles, the probability of drawing a blue marble is 4/7, and if you replace the marble, the probability remains 4/7 for the second draw.