probability with replacement of items please help

moharsingh

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Two cards are drawn at random with replacement from a box which contains 4 cards numbered 1,1,2 and 2.If X denotes the sum of numbers shown on the two cards,find the expected value of X.
 
Two cards are drawn at random with replacement from a box which contains 4 cards numbered 1,1,2 and 2.If X denotes the sum of numbers shown on the two cards,find the expected value of X.
What values do you expect after the two draws? In what proportions? Where are you stuck?

Please be complete. For instance, if you started by making a table showing the possible outcomes and their relative frequencies, please show that table. Thank you! ;)
 
Two cards are drawn at random with replacement from a box which contains 4 cards numbered 1,1,2 and 2.If X denotes the sum of numbers shown on the two cards,find the expected value of X.
This is just a matter of doing straightforward calculation. The probability you will draw a "1" on either draw is 1/2 and the probability you will draw a "2" is also 1/2. The only possible sums of two such numbers are "2", "3", and "4". To get a sum of "2" you must draw a 1 each time. What is the probability of that? To get a sum of "3" you must draw "1 then 2" or "2 then 1". What is the probability of each of those? To get a sum of "4" you must draw a "2" each time. What is the probability of that?
 
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