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Q#2:There are 50 tiles of which 15 are A's in a scrabble game. What is the probability of getting both A's when two tiles are drawn?

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2 Answers

3/35 = 8.57142 % or about 86 times out of 1000.
The reason these are dependent events is that once an "A" has been drawn, it reduces the number of "A"s remaining to be drawn and it reduces the number of tiles from which the next tile can be drawn.
If, having drawn an "A", it was then replaced in the tiles from which the next tile was to be drawn, these would be independent events and the probability of drawing two "A"s would then be (15/50)*(15/50)= 0.09 or slightly greater than if the two events were dependent.  This would be exactly 90 times out of 1000 or 9 times out of 100..

If the outcome of one event affects the outcome of another, then the events are said to be Dependent Events.
Event 1:  The probability of getting tile with letter "A" is 15/50 = 3/10
Event 2. Suppose, that first time we got an A. Then, the probability of getting "A" second time is 14/49 = 2/7
3. The probability of getting the tiles with "A" is (3/10)×(2/7) = 6/70 = 3/35
P(event 1, event 2) = 3/35