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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,
Thanks a lot but can u explain it a bit more
Q. there are two bags A and B; bag A contains 2 white and 3 black balls; bag B contains 3 white and 4 black balls. A bag is chosen at random find the probability that the ball drawn is white.