- #1
rymatson406
- 3
- 0
A box contains 2 red, 4 white, and 4 green two balls are drawn in succession without replacement. What is the probability that both balls are the same color?
Last edited:
rymatson406 said:A box contains 2 red, 4 white, and 4 green two balls are drawn in succession without replacement. What is the probability that both balls are the same color?
The probability of drawing two same-colored balls from a box depends on the total number of balls in the box and the number of balls of each color. For example, if there are 10 red balls and 10 blue balls in the box, the probability of drawing two red balls would be (10/20) x (9/19) = 0.2368 or 23.68%.
The number of balls in the box directly affects the probability of drawing same-colored balls. As the number of balls increases, the probability of drawing same-colored balls decreases. This is because there are more options to choose from, making it less likely to draw two balls of the same color.
If the drawn ball is replaced back into the box, the probability of drawing same-colored balls remains the same for subsequent draws. This is known as sampling with replacement, where each draw is independent of the previous one.
Yes, the probability of drawing same-colored balls can be greater than 50%, depending on the number of balls of each color in the box. For example, if there are 20 red balls and only 1 blue ball in the box, the probability of drawing two red balls would be (20/21) x (19/20) = 0.9048 or 90.48%.
No, the probability of drawing same-colored balls is not affected by the order in which the balls are drawn. This is known as sampling without replacement, where each draw affects the probability of the subsequent draws. However, as the number of draws increases, the impact of the order diminishes and the overall probability approaches a steady value.