Rosalie tosses a coin a number of times and counts the total

Question

Rosalie tosses a coin a number of times and counts the total number of times the coin lands tail-side up. How many times does she toss the coin?

 (1) The chance that the coin lands tail-side up exactly once is between 0.1 and 0.2.

 (2) The chance that the coin lands head side up exactly once is the same as the chance that the coin lands tail-side up exactly once

tapan22 · Answer

This is a hard one.

Is it E? (I get this funny feeling it might be C)

 #Tails/2*#flips = P(Tails)-----> We need, # of Flips 

st1: Does not really give us a specific value

St2: basically says for every 1H/2*flips = 1T/2*flips not sure if this tells us much.

Hope one of the other folks has a better explanation

fireboll · Answer

A.

st1.
The probability to show only one tail is n / 2^n,
and n should be 5 to place the chance between 0.1 and 0.2.
The number of coin throwing is 5.

st2.
The two chances are always the same.

tl372 · Answer

I'll go with A

St. 1
The probability of getting ANY combination of H and T is always (1/2)^N where n is the number of times a coin is tossed.

If the prob of getting 1 tails is b/w 0.1 & 0.2, then the coin must have been tossed 3 times:

1/2 * 1/2 * 1/2 = 0.125. Sufficient

*Notes, this is also the same probability of getting tails twice, or three times in a row. 

St. 2

The prob of 1 H is the always the same as the probability of 1 T if the # of throws are the same. Thus, it's insufficient.

Consider:
HHT - (1/2) ^3
TTH - (1/2) ^3

HHHT - (1/2)^4
TTTH - (1/2)^4

paddyboy · Answer

C.

1) What if the coin is doctored? The assumption that heads/tails have equal probability does not stand. Not sufficient.

We get 0.1 < p^n < 0.2; where n=no. of tosses;p=probablility of getting tails side up.

2) We are told that p = 0.5; however, it is insufficient in itself.

Combining the two, we get 0.1 < (0.5)^n < 0.2; and we get n = 3

tl372 · Answer

Is this something we can't assume? Not sure if on the real gmat they would ncessarly test something like this...

ps_dahiya · Answer

I don't think we have to assume these things.

shobhitb · Answer

OA is A. Great job fireboll, tl372!

paddyboy · Answer

I don't agree with the OA.

You would assume that the coin has perfectly equal probability if there was no other way of solving the problem. However, many math texts specify that "x tossed a perfectly weighted coin n times" in problems to specifically remove this doubt.

I would assume, therefore, that if this condition is specified, it should be factored into the solution.

:!:

Real world: There is no such thing as a perfectly weighted coin. Due to the different engravings on both sides, one of the sides would have a slightly greater probability of appearing...

Real world: There is no such thing as a perfectly weighted coin. Due to the different engravings on both sides, one of the sides would have a slightly greater probability of appearing...

ps_dahiya · Answer

Somethings are implicit and will not be stated on the exam. Apart from this, there are so many things that are valid in real life but in GMAT world. We go the test with the rules that are there, not with the rules we want.

paddyboy · Answer

Before I get any more recriminations, that "Real World" bit is not a support for my argument - I just put it in...

And regarding 'implicit' - why would someone specify a supposedly implicit condition on a DS. A case of 'The lady doth protest too much, methinks...'

What I'm trying to say is, implicitness would be dependent on the situation... what is implicit somewhere, may not be implicit elsewhere.

ps_dahiya · Answer

There are few examples: 1. All numbers are real unless stated. So if you don't see any statement about numbers then they are real. 2. Co-ordinate system is a two plane system unless stated. You may question GMAC to state these explicitly in every question but then you may be doing only 5-10 question in 75 minutes. Just my 0.02 cents. I agree with this:"implicitness would be dependent on the situation... what is implicit somewhere, may not be implicit elsewhere" But this more of a philosophical statement and doesn't apply in Quant, but may apply in verbal. :-D

paddyboy · Answer

Real World: Philosophy is universal... :-D Just Joking...

I still don't agree, but then as Voltaire said, "I disapprove of what you say, but I will defend to the death your right to say it."

Lets stop :hammer and start :drinking 

What would this board be without smileys...

Rosalie tosses a coin a number of times and counts the total

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