IB Statistics and Probability Problem 005
Bag \(A\) contains three white balls and four red balls.
Two balls are chosen at random without replacement.
Copy and complete the following tree diagram. (Do not write anything on this page.)
Find the probability that two white balls are chosen.
Bag \(B\) contains four white balls and three red balls.
When two balls are chosen at random without replacement from bag \(B\), the probability that they are both white is \(\frac{2}{7}\).
A standard die is rolled. If a \(1\) or \(2\) is obtained, two balls are chosen at random without replacement from bag \(A\), otherwise they are chosen from bag \(B\).
- Find the probability that both balls are white.
- Given that both balls are white, find the probability that they were chosen from bag \(A\).