If two candies are randomly drawn from the bag with replacement, there are 5 x 5 = 25 possible outcomes, since there are 5 possible colors for each candy.
To find the probability that the two candies are the same color, we can consider the following cases:
- Case 1: Both candies are brown. The probability of drawing a brown candy on the first draw is 0.3, and the probability of drawing another brown candy on the second draw is also 0.3. Therefore, the probability of both candies being brown is 0.3 x 0.3 = 0.09.
- Case 2: Both candies are red. The probability of drawing a red candy on the first draw is 0.2, and the probability of drawing another red candy on the second draw is also 0.2. Therefore, the probability of both candies being red is 0.2 x 0.2 = 0.04.
- Case 3: Both candies are yellow. The probability of drawing a yellow candy on the first draw is 0.2, and the probability of drawing another yellow candy on the second draw is also 0.2. Therefore, the probability of both candies being yellow is 0.2 x 0.2 = 0.04.
- Case 4: Both candies are green. The probability of drawing a green candy on the first draw is 0.2, and the probabilityof drawing another green candy on the second draw is also 0.2. Therefore, the probability of both candies being green is 0.2 x 0.2 = 0.04.
- Case 5: Both candies are orange. The probability of drawing an orange candy on the first draw is 0.1, and the probability of drawing another orange candy on the second draw is also 0.1. Therefore, the probability of both candies being orange is 0.1 x 0.1 = 0.01.
Adding up the probabilities of all these cases gives us the total probability of drawing two candies of the same color:
0.09 + 0.04 + 0.04 + 0.04 + 0.01 = 0.22
Therefore, the probability that two candies drawn from the bag with replacement are the same color is 0.22, or answer choice (B).