Final answer:
The probability that the balls are of same color is 52/100, or 0.52.
Step-by-step explanation:
To find the probability that two balls drawn at random from a bag are of the same color, we need to consider two scenarios: drawing two white balls and drawing two black balls.
Let's start with the probability of drawing two white balls. The bag initially contains 6 white and 4 black balls, so the probability of drawing a white ball on the first draw is 6/10.
After replacing the first ball, the bag still contains 6 white and 4 black balls, so the probability of drawing a white ball on the second draw is also 6/10.
To find the probability of both events occurring, we multiply the individual probabilities:
(6/10) * (6/10)
= 36/100.
Similarly, for drawing two black balls, the probability on the first draw is 4/10, and after replacing the first ball, the probability on the second draw is still 4/10.
Multiplying these probabilities gives us (4/10) * (4/10) = 16/100.
To find the total probability, we add the probabilities of the two scenarios:
36/100 + 16/100
= 52/100
= 0.52.