Three persons, A, B, C are asked to toss a coin in succession. question continues?

Question

Three persons, A, B, C are asked to toss a coin in succession. A prize will be awarded to the first person to throw a head. Calculate the probability that no person will win the prize.....

If A wins B & C will never get a chance to toss the coin. Same as A fail to get Head B wins C will never get a chance to wins. (Note: A, B & C get only once chance to toss).. So 1/8 wont be the answer) ... Come on any one there to help me ?

Any Genius out there????????

Answer 1

The answer really is 1/8.

A throws first and assuming a fair coin, has a 1/2 chance of throwing a head, winning the prize and ending the game. There is a 1/2 chance of moving on to B.

The chance of B winning is then 1/2 (chance of getting this far) times 1/2 (chance of B throwing a head) = 1/4. Likewise 1/2 x 1/2 chance of getting this far but B also throwing a tail.

Assuming we get this far the chance of C throwing a head is 1/2 x 1/2 (chance of getting this far) x 1/2 (chance of head).

Summary:
Chance of A winning = 1/2
Chance of B winning = 1/2 x 1/2 = 1/4
Chance of C winning = 1/2 x 1/2 x 1/2 = 1/8
Chance of nobody winning = 1 - (1/2 + 1/4 + 1/8) = 1/8

Answer 2

1/8 is the answer ... but lets look at it this way ...

A wins if he throws a head so p(A wins)=1/2

B wins if A throws a tail and B throws a head P(B wins)=1/2*1/2=1/4

C wins if A nd B both throw tails and C throws a head =1/2 * 1/2 *1/2 = 1/8

So probability that someone wins is P(A wins) + P(B wins) + P(C wins) = 1/2 + 1/4 +1/8 = 7/8

So probability no one wins is 1/8.

This is also the possibility that all three throw a tail - the reason for this is that although B and C won't get a chance if A wins (etc), where they to have a chance they would throw either a head or a tail so by discounting both possibilities you end up with P(no one wins) = P(three tails - where three coins tossed) = 1/8

phew...

Answer 3

The chance that person A will throw heads is an even chance. As is the chance that B will throw heads. Also person C has an even chance of throwing heads. Each of the three has the same chance of throwing tails. There is an even chance that no one will throw heads. This is true even if 1,000,000 people have a throw. Now if you ask what are the chances of the coin landing on its edge, well that is a different matter. The three events are not connected and are each a single event. The prize could be won after the first, second or third throw or not at all. So the probability that no-one will win the prize remains the same - An even chance

Answer 4

1/8 is the answer...doesn't matter if B and C get a chance or not...there is only 1 way for NO one to get a prize. That is for all 3 coins to be tails.

A will win half the time....50%

Of the 50% that A loses...B will win half of those...or 25% of the total

Of the half that B loses (which is still 25% of the total) C will win half of those...or 12.5% of the total

A wins 50, B wins 25, C wins 12.5....that still leaves 12.5% with no winner.

Which is 1/8.

Answer 5

1 in 2.
A has 1 in 2 chance of getting a tail. If he gets a tail, and loses, then the other 2 don't get a chance to toss.

Answer 6

Your second paragraph is a red herring. It's 1/8.

There are 8 outcomes
hhh hht htt hth thh tht tth ttt

Just because if any of the first four happen the rest are moot doesn't change the odds. You're looking for ttt and that happens 1 out of 8 times.

Answer 7

for no one to win the price we need a combination of 3 scenarios
T=tail
1. t P(t) = 1/2
2. tt P(tt) = 1/2*1/2= 1/4
3. ttt P(ttt) = 1/2*1/2*1/2= 1/8

P(no one wins) = P(first doesn't)* P(of second doesn't)* P(of third doesnt)
= 1/2*1/4*1/8 = 1/64

Answer 8

Toss head matron nooooooooooo PS the answer is 11

Answer 9

prob that A loses is 1/2

prob that B loses is ( first A must lose & then B must lose )

= 1/2 * 1/2


prob that C loses is ( first A& B must lose & then C must lose )

= 1/2 * 1/2 * 1/2 = 1/8

Answer 10

We need three tails for no prize
1in2 for A
times 1in2 for B
times 1in2 for C = 1in8
thats 50%x50%x50% = 12.5% = 1in8 no prize