What is the probability of tossing ten dimes and getting 50% heads and 50% tails on one toss?
Don't know how the bot gots its wrong answer but .....
we want the prob(exactly 5 out of 10 to be heads)
prob heads = 1/2
prob tails (or non-heads) = 1/2
prob(of our event) = C(10,5) (1/2)^5 (1/2)*5
= 25*(1/2)^10 = 252/1024
= 63/256
= appr .2464
check:
prob(0 heads) = 1/1024
prob(1 head ) = 10/1024
prob(2 head) = 45/1024
prob(3 heads) = 120/1024
prob(4 heads) = 210/1024
prob(5 heads) = 252/1024 <------ ours
prob(6 heads) = 210/1024
prob(7 heads) = 120/1024
prob(8heads) = 45/1024
prob(9 heads) = 10/1024
prob(10 heads) = 1/1024
add them up and you get 1024/1024 = 1, yeahhhh!