Question

A fair coin tossed 100 times what is the probability of getting a tail on tossing odd no of times

Answer 1

Answer:

1/2

I hope this helps.

Step-by-step explanation:

P(odd number of tails)

= P(1 tail) + P(3 tails) + P(5 tails) + ... + P(99 tails)

It's not obvious that this is going to be one half.  The problem is that there is an even number of tosses.  Let's look at 99 tosses then and build up from there.

99 tosses

P(odd number of tails)

= P(1 tail) + P(3 tails) + ... + P(99 tails)

= P(1 head) + P(3 heads) + ... + P(99 heads)     [ because heads and tails are equally likely ]

= P(98 tails) + P(96 tails) + ... + P(0 tails)

= P(even number of tails)

But P(odd number of tails) + P(even number of tails) = 1, so

P(odd number of tails) = P(even number of tails) = P(odd number of heads) = P(even number of heads) = 1/2

Back to 100 tosses

P(odd number of tails in 100 tosses)

= P(odd number of tails in 100 tosses with last toss being a head)

 + P(odd number of tails in 100 tosses with last toss being a tail)

= P(odd number of tails in first 99 tosses) × P(100th toss is a head)

 + P(even number of tails in first 99 tosses) × P(100th toss is a tail)

= (1/2)×(1/2) + (1/2)×(1/2)

= 1/4 + 1/4

= 1/2