Alper, Beatta, and Grandma each pick ﬁve cards from a shuﬄed standard deck. Alper replaces the...

Alper, Beatta, and Grandma each pick ﬁve cards from a shuﬄed standard deck. Alper replaces the card and reshuﬄes each time he picks. Beatta picks from the deck without replacement. Grandma repeatedly picks the top card from the deck and puts it back on the top of the deck. Count an ace as 14, a king as 13, and so on. Let X,Y,Z be the sum of the numbers Alper, Beatta, and Grandma get, respectively. Which of X,Y,Z has or have the largest expected value?

Expert Solution

They all the same expectation. The proof is done in the images below :

orchestra answered 2 years ago

Alper, Beatta, and Grandma each pick ﬁve cards from a shuﬄed standard deck. Alper replaces the...

Alper, Beatta, and Grandma each pick ﬁve cards from a shuﬄed standard deck. Alper replaces the card and reshuﬄes each time he picks. Beatta picks from the deck without replacement. Grandma repeatedly picks the top card from the deck and puts it back on the top of the deck. Count an ace as 14, a king as 13, and so on. Let X,Y,Z be the sum of the numbers Alper, Beatta, and Grandma get, respectively. Which of X,Y,Z has or...

Alper, Beatta, and Grandma each pick five cards from a shuffled standard deck. Alper replaces the...

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Alper, Beatta, and Grandma each pick ﬁve cards from a shuﬄed standard deck. Alper replaces the...

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