Question

There are 18 marbles in a bag, all of the same size. The marble; red, green and blue are in the ratio 2:3:4 respectively: if two marbles are selected at random one after the other and replaced, find the probability that they are of the same colour

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to determine the total number of ways to select 2 marbles out of 18, which can be calculated using the combination formula:

Total number of ways = 18C2 = 153

Next, we need to find the number of ways to select 2 marbles of the same color. Since the marbles are in the ratio of 2:3:4 for red, green, and blue respectively:

- Number of ways to select 2 red marbles = 2C2 = 1
- Number of ways to select 2 green marbles = 3C2 = 3
- Number of ways to select 2 blue marbles = 4C2 = 6

Therefore, the total number of ways to select 2 marbles of the same color = 1 (red) + 3 (green) + 6 (blue) = 10

Finally, the probability of selecting 2 marbles of the same color can be calculated as:

Probability = Number of ways to select 2 marbles of the same color / Total number of ways
Probability = 10 / 153
Probability ≈ 0.06536

Therefore, the probability that two marbles selected at random will be of the same color is approximately 0.06536 or 6.536%.