A box contains 6 yellow, 5 violet & 3 pink chips. If 3 chips are tobe selected in random, what is the probability that the chips are composed of 2 violet or 1 pink?
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To find the probability, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
We need to consider two scenarios: either selecting 2 violet chips or selecting 1 pink chip.
1) Selecting 2 violet chips:
Since there are 5 violet chips in the box, we can select 2 violet chips in 5C2 ways (using the combination formula). The number of ways to select 2 chips from 5 is calculated as:
5C2 = (5!)/(2!(5-2)!) = 10.
2) Selecting 1 pink chip:
Since there are 3 pink chips in the box, we can select 1 pink chip in 3C1 ways (using the combination formula).
3C1 = (3!)/(1!(3-1)!) = 3.
Now, let's calculate the total number of possible outcomes:
We need to select 3 chips from a total of 6 yellow, 5 violet, and 3 pink chips. Therefore, the total number of possible outcomes is given by:
(6 + 5 + 3)C3 = 14C3 = (14!)/(3!(14-3)!) = 364.
Now, let's calculate the probability:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = (10 + 3) / 364
Probability ≈ 0.0357 (rounded to four decimal places) or 3.57% (rounded to two decimal places).
Therefore, the probability that the chips are composed of 2 violet or 1 pink is approximately 0.0357 or 3.57%.