There are $15$ urns of $3$ different kind, filled with black and white balls, given in the table:
kind | amount | black balls | white balls
----------------------------------------------
I | 2 | 10 | 15
II | 6 | 8 | 2
III | 7 | 10 | 6
One of these urns will be chosen randomly and equally distributed. From this urn, a ball is picked randomly and equally distributed. It is a black ball. What's probability that it came from an urn of kind I?
I have idea but not know if idea is good.
I first need know what is probability that black ball is from urn I.
Probability is $\frac{10}{25}$
Now need to be careful because we have in total $15$ urns and from these $15$ urns we have $2$ times the urn I.
In end we have probability to get black ball from urn I: $$\frac{2}{15} \cdot \frac{10}{25}= \frac{4}{75} \approx 0.05\bar{3} \approx 5.33\text{%}$$
Is it good or not? Pls need info for test next week.