Question

What is the probability that 19 independent tosses of an unbiased coin result in no fewer than 1 head and no more than 18 heads?

Answer 1

compute the probability you get
no heads
19 heads
add them up and subtract the result from one

Answer 2

"no few than one head" means you did not get 0 heads (all tails)
"no more than 18 heads" means you did not get 19 heads

Answer 3

so 1-(1/2)^19

Answer 4

\[P(0)=\frac{1}{2^{19}}\]

Answer 5

close you have to subtract that off twice, once for no heads and once for all heads

Answer 6

\[1-2\times \frac{1}{2^{19}}\]

Answer 7

or maybe instead
\[1-\frac{1}{2^{18}}\] it will be very close to one

Answer 8

i get 0.999996185302734375

Answer 9

so You are looking for this interval(1-18)

Pr(1<=x<19) so you are looking for the probability 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18

Pr(x=1)+.......Pr(x=6)+................+Pr(x=18)
it will be hard to calculate all the probabilities (1-18) so the best choice is here is to go to the complement probability

the complement would be gettin 0 heads or 19 heads

Pr(x=0)=0.5^19=1.90*E-6 very vey very smal number
Pr(x=19)=0.5^19=1.90*E-6

The sum of these two gives u the complement Probability

Prc=2*1.90*E-6

So the answer here would be 1-2*1.90*E-6

===0.9999961853

Answer 10

so @satellite73 is correct