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Answer :
The probability of all three balls selected is 0.138.
How To find the probability that all three balls selected without replacement are purple?
We need to calculate the ratio of the number of favorable outcomes (selecting three purple balls) to the total number of possible outcomes.
The total number of balls in the urn is:
Total balls = 3 (small pink balls) + 10 (small purple balls) + 6 (small white balls) = 19
To calculate the probability of selecting a purple ball on the first draw, we have 10 purple balls out of the 19 total balls.
Therefore, the probability of drawing a purple ball on the first draw is:
P(purple on first draw) = 10/19
After the first purple ball is drawn, there are now 9 purple balls remaining out of 18 total balls.
So, the probability of drawing a purple ball on the second draw, given that the first ball was purple, is:
P(purple on second draw) = 9/18
Similarly, for the third draw, after two purple balls have been drawn, there are 8 purple balls remaining out of 17 total balls.
The probability of drawing a purple ball on the third draw, given that the first two balls were purple, is:
P(purple on third draw) = 8/17
To find the probability of all three events happening (drawing three purple balls in a row), we multiply the probabilities of each individual event:
P(all three balls are purple) = P(purple on first draw) * P(purple on second draw) * P(purple on third draw)
P(all three balls are purple) = (10/19) * (9/18) * (8/17)
Calculating this expression:
P(all three balls are purple) ≈ 0.138 (rounded to the nearest hundredth)
Therefore, the probability that all three balls selected without replacement are purple is approximately 0.138.
Learn more about probability
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