An urn contains 5 balls, two which are marked $1, 2 balls$ 5, and one$15. A game is played by paying$ 10 for winning the sum of the amounts marked on two balls selcted randamoly from urn. Is this a fair game.
2007-06-25 13:19:57 · 2 answers · asked by Anamika 2 in Science & Mathematics ➔ Mathematics
There are 20 possible results from drawing 2 balls. Labeling the balls as:
1a, 1b, 5a, 5b and 15, the combinations are
1a+1b, 1a+5a, 1a+5b, 1a+15
1b+1a, 1b+5a, 1b+5b, 1b+15
5a+1a,5a+1b. 5a+5b, 5a+15
5b+1a, 5b+1b.5b+5a, 5b+15
15+1a, 15+1b, 15+5a, 15+5b
The average value of the sum of the 2 balls drawn is the sum
of all 20 two ball combinations divided by the total number of possible combinations (20). The average is 9.25. Thus, if you pay $10 to draw two balls, you will lose on average $0.75. This is not a fair game.
2007-06-25 13:43:28 · answer #1 · answered by Marv S 1 · 0⤊ 0⤋
Yes. You stand to win more tha you would lose.
2007-06-25 20:29:14 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋