an urn contains 3 blue chips and 7 red chips. sequentially draw 3 chips without replacement. what is the probability that all drawn chips will not be the same color?
there are 10C3 ways of drawing 3 chips
there are 7C3 ways of drawing 3 red chips
there is one way to draw 3 blue chips
p = 1 - [(7C3 + 1) / 10C3]
To find the probability that all drawn chips will not be the same color, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
In the first draw, there are 10 chips in the urn. In the second draw, there are 9 chips remaining since we are drawing without replacement. In the third draw, there are 8 chips remaining. So the total number of possible outcomes is given by:
10 * 9 * 8 = 720
Number of favorable outcomes:
For the first chip, we can choose any of the 10 chips. For the second chip, we need to choose a chip of a different color from the first one. So there are 7 possible choices. Finally, for the third chip, we need to choose a chip of the third color. There are 3 remaining chips of the third color. So the number of favorable outcomes is given by:
10 * 7 * 3 = 210
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 210 / 720
Probability ≈ 0.2917
Therefore, the probability that all drawn chips will not be the same color is approximately 0.2917 or 29.17%.