Suppose you are playing a game of chance. If you bet $6 on a certain event, you will collect $174
(including your $6 bet) if you win. Find the odds used for determining the payoff.
A) 174 : 180
B) 1 : 28
C) 29 : 1
D) 28 : 1
A set consist of 2n-1 element. What is the number of subsets of this set which contain at most n-1 elements?
B. 2^(2n) - 2
C. 2^(2n) -1
Could someone please help with the above questions. thanks!
hey your solution helps I think. In a 2n-1 binomial expansion there will be 2n terms ( ie 2n-1C0 to 2n-1C2n-1) but in our expansion we need the terms only uptil n-1, like you've done above- so that makes it half of the total number of terms in the binomial expansion. since the entire expansion= 2^2n-1, the first half of the expansion will be equal to (2^2n-1)/2 which gives 2^2n-2. Right? the answer is a) and i think this logic is correct. please verify.
@arushi ...I think I got the notion behind this ques.....let A be the event of winning then P(A)+P(A')=1
Then the in favour of winning is given by p(A)/p(A')
Now in terms of payoff ....the payoff when event A occurs is 174-6=168! Because we are considering payoff not total profit
The payoff associated with not winning to the gambler other side is 6. So,
Which is read as if u bet with 6 nd if u win u'll get 168 as payoff and the betting amnt of 6 nd if u loose the gambler will take ur betting amnt ie 6
you bet 6 and after winning you get 174. By logic, in any game of chance payoff are kept in that way that u can't win in long run(otherwise casinos won't be profitable). Since, in this case if every chance u are betting 6
so if u bet 174/6 = 29 times ur net profit would be zero (u will win 1 time and loose 28 times) in long term that means ur probability to win is 1/29. So, for casino odds for determining payoff would be (odds favoured/ odds against)= 28/1.
and for me odds for winning would be 1/28 while probability for winning is 1/29.
answer would be 2^(2n-2).
u have to divide the sum of series of (2n-1)C0+(2n-1)C1+..........+(2n-1)C(2n-1) by 2 .
sum of series = 2^(2n-1) and now divide by 2.