Respuesta :
Answer:
There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.
There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.Thus the expectation for winning is about $0.30 and losing very close to $1...the t total expectation is about -$0.70.
There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.Thus the expectation for winning is about $0.30 and losing very close to $1...the t total expectation is about -$0.70.You can calculate the exact number by using the exact probability of picking the winning number stated in the first line of this answer.
Step-by-step explanation:
I hope it's helpful
Answer: Expected Value = -0.95 approximately
Interpretation: On average, we lose about 95 cents each time we play the game.
This is not a fair game because the expected value is not 0.
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Explanation:
There is only one way to win the game which is to match all the numbers.
This is out of 376,740 different ways to select 6 items from a pool of 28. The steps on how to get this value are shown below
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{28} C _{6} = \frac{28!}{6!*(28-6)!}\\\\_{28} C _{6} = \frac{28!}{6!*22!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23*22!}{6!*22!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23}{6!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23}{6*5*4*3*2*1}\\\\_{28} C _{6} = \frac{271,252,800}{720}\\\\_{28} C _{6} = 376,740\\\\[/tex]
I used the nCr combination formula. n = 28 is the pool size and r = 6 is the sample size.
Therefore, the probability of winning is 1/376740 and the probability of losing is 1-1/(376740) = 376739/376740
Multiply the odds found by each corresponding net winnings
Win: (1/376740)*(20,000) = 0.05308700960874
Lose: (376739/376740)*(-1) = -0.99999734564951
Then add up those results
0.05308700960874 + (-0.99999734564951) = -0.94691033604078
Rounding to the nearest cent, we get -0.95
The expected value is -0.95
We expect to lose, on average, 95 cents every time we play the game. The game is considered not fair because the expected value is not 0. The game is in favor of the lotto company.
