Question

FIR coin is tossed hundred times the probability of getting two tails 1,3 ,.......,49 times is​

Answer 1

Answer:

Step-by-step explanation:

Let p= probability of getting a tail in a single trial =1/2 ,

n= number of trails =100 ,

and X= number of tails in 100 trials.

We have,

P(X=r)= 100 C r , p r , q n-r,

100 C r(1/2)r (1/2)100-r,

=100 C r(1/2)100,

Now,

P(X=1)+P(X=3)+....+P(X=49),

=100 C 1(1/2)100 + 100 C 3(1/2)100 + .... + 100 C 49(1/2)100,

=(100 C 1+100 C 3+....+100 C 49)(1/2)100,

=But , 100 C 1 + 100 C 3 + .... + 100 C 99,

=2∧99,

Also, 100 C 99=100 C 1,

100 C 97=100 C 3, .... 100 C 51,

=100 C 49,

Thus,

2(100 C 1 + 100 C 3 + .... + 100 C 49),

=2∧99,

⇒100 C 1 + 100 C 3 + .... + 100 C 49,

=2∧98,

∴ Probability of required event,

= 2∧98/2∧100,

⇒1/4.

Hope it helps.