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Formula used for sum of cards probability problem

Formula used for sum of cards probability problem

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https://365datascience.teachable.com/courses/506102/lectures/9302985
Here at 1.45, it is mentioned expected value is p(2)*2 +p(3)*3……..
where ‘2’ and ‘3’ are no of times ‘2’ and ‘3’ featured in the table.
in the frequency distribution table ‘2’ features one time and ‘3’ features ‘2’ times
so it should be p(2)*1+p(3)*2…. e.t.c
Please clarify

1 Answer

365 Team
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Hey Amar, 
 
Thanks for reaching out!
 
If you go back, you’ll see that we’re saying that we take the number of times each value appears in the table to determine the probability of each outcome. Hence, the table helps us find p(2), rather than 2. 
 
Hence, it’s the sum of the product between the likelihood of an outcome p(x) and it’s value x. Hence, we have p(2)*2 + p(3)*3 + … + p(12)*12 = (1/36) * 2 + (2/36) * 3 + … + (1/36) * 12 and so on. 
 
Best,
365 Vik