Probability problem

I am stuck, kindly help.

There are two men V1 and V2. Each man has two buckets A and B. Bucket A contains numbered blocks from 7 to 14. Bucket B contains numbered blocks from 15 to 30.
V1 and V2 can pick any numbered block (X) with a uniform probability from any bucket (A or B). However, the probability of selecting bucket A is 0.6 while probability of selecting bucket B is 0.4.
I want to know what is the probability that V1 and V2 select an identical numbered block, if they operate independently.
Also, what would be the expectation of X in this case
A stepwise formulation would be very helpful.

Calculate each of the following probabilities:

1. A specific block is picked from a specific bucket.
2. Both men pick bucket A.
3. Both men pick bucket B.
4. Both men pick the same bucket.
5. Given that both men pick bucket A, they pick the same block.
6. Given that both men pick bucket B, they pick the same block.
7. Given that both men pick the same bucket, they pick the same block.

Do you know how to calculate at least some of the above?

The expectation is the sum of the value of each block weighted by the probability of it being picked.


TS Contributor
a sytematic approach would be to apply the total probability formula:

P(id) =P(id| AA) *P(AA) + P(id|AB)*P(AB) + P(id|BA)*P(BA) + P(id|BBj * P(BB)

Where P(id|AA) is the conditional probability of picking an identical number if both pick bucket A and P(AA) is the probability that both pick bucket A and so on.