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Benjiman has a stack of 10 cards, 8 of which are labeled "3" and the other 2 labeled "9".

a. What is the expected value when he picks a random card from the stack?

b. What is the expected value when he adds one additional "9" to the stack?(and then draws one randomly)

c. What is the expected value when he adds two additional "9s" to the stack?(and then draws one randomly)(10 "9s")

d. What is the number of  "9s" that he has to add before the expected value is at least?

Jun 17, 2020

#1
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a)  Since the deck contains 8 cards labeled "3" and 2 cards labeled "9",

the total value of the cards is:  8 · 3 + 2 · 9  =  24 + 18  =  42.

The expected value of one randomly drawn card is  42 / 10  =  4.2.

b)  An additional "9" is added to the deck: the total value is now:  8 · 3 + 3 · 9  =  24 + 27  =  51.

The expected value is now  51 / 11  =  4.64    (approximately)

Are these two addition cards added immediately after step a or after step b?

If they are added after step b, the totall value is now:   8 · 3 + 5 · 9  =  24 + 45  =  69.

The expected value is now:  69 / 13  =  5.31

d)  This question is incomplete.

Jun 17, 2020
#2
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Oh sorry problem d) What is the number of  "9s" that he has to add before the expected value is at least 8?