Question

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,I solved this and got a 71 over 105

Answer 1

To find the probability that both balls picked are of different colors, we need to consider all possible outcomes.

Total number of balls in the basket = 3 red + 5 blue + 7 green = 15 balls

First, let's find the probability of picking a red ball on the first pick:
Probability of picking a red ball = Number of red balls / Total number of balls
= 3 / 15
= 1 / 5

After picking a red ball, there are 14 balls left in the basket (since we did not replace the red ball). So, the probability of picking a ball of a different color (blue or green) on the second pick is:
Probability of picking a blue ball = Number of blue balls / Total number of remaining balls
= 5 / 14

OR

Probability of picking a green ball = Number of green balls / Total number of remaining balls
= 7 / 14
= 1 / 2

Since we are interested in the probability of picking a ball of a different color on the second pick, we need to consider both probabilities and add them together:

Total probability = Probability of picking a red ball on the first pick * Probability of picking a blue ball on the second pick
+ Probability of picking a red ball on the first pick * Probability of picking a green ball on the second pick

Total probability = (1 / 5) * (5 / 14) + (1 / 5) * (7 / 14)
= 1 / 14 + 7 / 70
= 5 / 35 + 7 / 70
= 12 / 70

Simplifying this fraction, we get:
Total probability = 6 / 35

Therefore, the probability that both balls picked are of different colors is 6 / 35.