Asked by Macy
A deck of cards has the aces and face cards removed, so that the numbered cards 2-10 remain. The player draws a card and is paid the value of the card. Each play costs $5. If you play the game 20 times, how much money would you expect to win or lose overall?
I started to make a probability table with the x and p(x) labeled but i don't know how to continue from here.
I started to make a probability table with the x and p(x) labeled but i don't know how to continue from here.
Answers
Answered by
bobpursley
There are 9x4 cards in the deck. All are equally probable.
if you get a 2, you lose 3 dollars
3...lose 2 dollars
4..lose 1 dollar
5 break even
6 win 1
7 win 2
8 win 3
9 win 4
10 win 5
The mean win is 1.50 per play, in 20 plays, that is 30 dollars.
if you get a 2, you lose 3 dollars
3...lose 2 dollars
4..lose 1 dollar
5 break even
6 win 1
7 win 2
8 win 3
9 win 4
10 win 5
The mean win is 1.50 per play, in 20 plays, that is 30 dollars.
Answered by
Reiny
The prob of drawing any specific number is 4/36 = 1/9
expected return on one game
= expectation(2) + expectation(3) + ... + expectation(10)
= (1/9)(2) + (1/9)(3) + ... + (1/9)(10)
= (1/9)(2+3+4+...+10)
= (1/9)(45) = 5
so it will cost 20($5) or $100 to play the 20 games
the expected return is 20($5).
So you will break even.
expected return on one game
= expectation(2) + expectation(3) + ... + expectation(10)
= (1/9)(2) + (1/9)(3) + ... + (1/9)(10)
= (1/9)(2+3+4+...+10)
= (1/9)(45) = 5
so it will cost 20($5) or $100 to play the 20 games
the expected return is 20($5).
So you will break even.
Answered by
Argghh - correction - Reiny
2+3+4+..+10 = 54 , not 45
so the expected return is (1/9)(54) = $6
so cost to play 20 games = 100
return = 20(6) = 120
so you would expect a profit of $20 to play 20 games
so the expected return is (1/9)(54) = $6
so cost to play 20 games = 100
return = 20(6) = 120
so you would expect a profit of $20 to play 20 games
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.