top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

A fair coin is tossed until a head comes up for first time. What is the probability of this happening on an odd tosses?

0 votes
523 views

A fair coin is tossed until a head comes up for the first time. What is the probability of this happening on an odd number tosses?

posted Jun 26, 2018 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

1 Answer

0 votes

Required Probability = 1/2(First coin turns heads) + 1/2^3 (third coin turns heads) + 1/2^5(Fifth coin turns heads + ..........
Required Probability = 1/2 + 1/2^3 + 1/2^5 + 1/2^7 + 1/2^9 ........
Required Probability = 1/2(1-(1/4)) = 2/3.

answer Jun 28, 2018 by Tejas Naik



Similar Puzzles
+1 vote

A tosses a fair coin 50 times. B tosses another fair coin 51 times. What is the probability that B got more heads than A?

0 votes

Sachin has two coins, one of Rs. 1 denomination and the other of Rs. 2 denomination. He tosses the two coins simultaneously. What is the probability that he gets at least one head?

0 votes

If you toss a coin ten times and it lands heads up every time, what is the probability that it will land heads up if you toss it again?

0 votes

You are playing a probability game with your friend using a fair coin. Both of you decide on a particular sequence that you have to achieve.

Let us suppose you chose the sequence to be: H T H
Your friend chose the sequence to be: H T T

Now you keep tossing coins until you get the sequence and the same is done by your friend. You keep doing that till you achieve your predefined sequence and keep writing the result on paper. At the end of the game the player whose average number of tosses will be lowest, he will win.

The results of the game 1 toss:
You: H T T H T H
Your score: 6
Your friend: H T H H H T H H T T
Your friends’ score: 10

The results of the game 2 toss:
You: T T H T T H H T H
Your score: 9
Your friend: T T H H T H T T
Your friends’ score: 8

The results of the game 3 toss:
You: T T H H T H
Your score: 6
Your friend: H H T H T T
Your friends’ score: 6

Now after 3 games, your average score is 7 and your friend’s average score is 8. Now assume that you keep playing the game and play many times. What will be the possible outcome of the following?

a) You win
b) Your friend win
c) Tie

...