What is the Probability of Drawing a Black Ball from Two Urns?

[oufa]

hi
i have an exam after 1 week and while i was studying i found this simple problem
but i couldn't answer it as the author
it is


We have two urns, I and II. Urn I contains 2 black balls and 3 white
balls. Urn II contains 1 black ball and 1 white ball. An urn is drawn at random
and a ball is chosen at random from it. We can represent the sample space of this
experiment as the paths through a tree as shown in Figure 4.1. The probabilities
assigned to the paths are also shown.
Let B be the event “a black ball is drawn,” and I the event “urn I is chosen.”
Then the branch weight 2/5, which is shown on one branch in the figure, can now
be interpreted as the conditional probability P(B|I).



any one please tell me why it is 2/5 because i think it is 1/5
figures mentioned arenot important in solving it

thnx for help

 

[HallsofIvy]

Why do you think it should be 1/5 and why do you think the figures are not important?

The "branch weight" is 2/5 precisely because urn I contains 5 balls, 2 of which are black.