hi ashmath

I'll try.

Firstly, go back to the definition:

So, how to work out the total number of outcomes?

My approach is to imagine the 'experiment' is repeated again and again until every event has had a fair chance to occur. The key here is what do I mean by a fair chance.

For bag A there are 5 balls so I can get the probabilities just by saying 'total number of outcomes' = 5.

For bag B in the same way 'total number of outcomes' = 7

So how to fairly decide on the number when either bag may be picked.

If I pick from bag A 35 times (5x7) then P(W) = 14/35 and P(B) = 21/35

and for bag B, I would get P(W) = 15/35 and P(B) = 20/35

So I can treat A and B fairly by having 35 trials for A and 35 trials for B.

So I'll have 70 trials altogether.

70 splits like this P(A) = 35/70 and P(B) = 35/70

Then use the probabilities above to get P(A & W) = 14/70 P(A & B) = 21/35 P(B & W) = 15/70 P(B & B) = 20/35

Then I can see that 'total number of outcomes' = 70

'Number of ways W happens' = 14 + 15 = 29

So P(W) = 29/70

Hope that helps,

Bob