To find the probability that both balls picked are of different colors, we can first find the probability of picking one red ball and one blue ball, or one red ball and one green ball, or one blue ball and one green ball.
1. Probability of picking one red ball and one blue ball:
- Number of ways to pick one red ball = 3
- Number of ways to pick one blue ball = 5
- Total number of ways to pick 2 balls = 15 (3 red + 5 blue + 7 green)
- Probability = (3/15) * (5/14) = 3/42 = 1/14
2. Probability of picking one red ball and one green ball:
- Number of ways to pick one red ball = 3
- Number of ways to pick one green ball = 7
- Total number of ways to pick 2 balls = 15
- Probability = (3/15) * (7/14) = 3/30 = 1/10
3. Probability of picking one blue ball and one green ball:
- Number of ways to pick one blue ball = 5
- Number of ways to pick one green ball = 7
- Total number of ways to pick 2 balls = 15
- Probability = (5/15) * (7/14) = 5/42
Now, we add the probabilities of picking one red and one blue ball, one red and one green ball, and one blue and one green ball:
(1/14) + (1/10) + (5/42) = 3/21 + 2/21 + 5/42 = 10/42 = 5/21
Therefore, the probability of picking two balls of different colors is 5/21.
A basket contains three red balls five blue balls and 7 green balls two balls are picked one after the other without replacement find the probability that both of different colors please solve step by step
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