111/3?
A has n+1 fair coins and B has n fair coins.If they toss all the coins , what is the probability that A gets more heads than B ?
-
UP 0 DOWN 0 1 12
12 Answers
24here it is................(plzz forgive me if it goes horribly wrong)
remove one coin from A's set.
now compare the first no. of heads in first n coins of A and n coins of B.
we get 3 cases(or outcomes)
1)A's n coins have more heads than B's n coins
2)A's n coins have equal no. of heads as B's n coins
3)B's n coins have more heads than A's n coins
we can see by symmetry that P(1)=P(3)
let P(1)=a=P(3) and P(2)=b
=> 2a+b=1
if case1 arises then (n+1)th coin will make no difference and A will surely get more heads.
if case3 arises then also (n+1)th coin will not make any diff. and A will get less heads when compared to B
but real thing happens in case 2
If (n+1)th coin is head(with prob 1/2) then A will have more heads than B.
=> Prob of A having more heads inc. by b/2
=> Total prob. of A having more heads =a+b/2=a+(1-2a)/2
=>a+0.5-a
=>0.5
62how about this simpler trick..
the probability of getting more heads = probability of having more tails!
hence the prob of getting more heads=prob of getting less no of heads
there cant be equal no of heads and tails..
hence.. prob=1/2!!!
so simple :P
33A and B have same chances for n tosses.... all depends on (n+1)th toss... so if A gets head there, he gets more heads so prob of getting head in (n+1)th toss =1/2
1@ nishant the statement
the prob of getting more heads=prob of getting less no of heads
is this statement really true ??????
my statement
A having more heads =A having less or equal heads