Answer:
The probability is P = 0.08
Step-by-step explanation:
We have:
2 pink balls
7 purple balls
6 white balls
So the total number of balls is just:
2 + 7 + 6 = 15
We want to find the probability of randomly picking 3 purple balls (without replacement).
For the first pick:
Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)
p₁ = 7/15
Second:
Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:
p₂ = 6/14
third:
Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:
p₃ = 5/13
The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:
P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13) = 0.08
