Marco and Maria toss a coin three times. Each time a head is

Question

Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria $1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has $1 less than he did before the 3 tosses?

it is an example with coins, without possible answer choices. please provide explanations.

it is an example with coins, without possible answer choices. please provide explanations.

LM · Accepted Answer

Marco can have 1 dollar less than he had before the 3 tosses only in one case, i.e., when there is "H" twice and "T" once.

THH = (1/2)^3
HTH = (1/2)^3
HHT = (1/2)^3

THH + HTH + HHT = 3/8

walker · Answer

3/8

Marco has $1 less than he did before the 3 tosses if we have 2 heads and 1 tail:
we use formula: p=nCm*p^m*q^(n-m)
where p - probability of a head
q - probability of a tail
m - the number of heads
n - the total number of tosses.

p=3C2*(1/2)^2*(1/2)=3/8

GMATBLACKBELT · Answer

We need a WLL scencario. it will be 1/2*1/2*1/2 --> 1/8

Now WLL --> 3!/2!1! --> 3 - the number of possible arrangements of WLL. So 3*1/8 -> 3/8

pmenon · Answer

for him to end up with a buck less means that the outcome was two heads and one tail. And this can happen in any order.

So, using binomial theorem, we get: (3C2)*(1/2)^2*(1/2) = 3*1/8 = 3/8

x2suresh · Answer

It should be two tails and 1 head.

3 WAYS possible = HTT+TTH+THT

PROBABILITY = 3/ 2^3=3/8

srivas · Answer

Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria $1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has $1 less than he did before the 3 tosses?

it is an example with coins, without possible answer choices. please provide explanations.

Soln: For Marco to lose one dollar, the possible events are (HHT,HTH,THH) = 3 ways
Total number of possibilites is = 2 * 2 * 2 = 8 ways

Thus probability that Marco loses 1$ is = 3/8

jeeteshsingh · Answer

Can only happen.. if we have two Heads and one Tails....

HHT = (1/2)^3 x 3!/2! (Arrange HTT) = 3/8

bangalorian2000 · Answer

For Marco to have 1$ less than he did before the 3 tosses so 2 heads and one tail have to come.
p(event) = p(h)*p(h)*p(t) + p(h)*p(t)*p(h) + p(t)*p(h)*p(h) = (1/2)^3 + (1/2)^3 + (1/2)^3 = 3/8

JeeMat · Answer

A combinatoric approach:

There are  2^3  total permutations of possible results.

The ones where he ends up with -1$ obviously consist of 2x head, 1x tails. We can calculate the number of ways this can happen (head, head, tails or head, tail, head etc.) with the formula
 \frac{P^3_3}{2!} = \frac{3!}{2!} = 3 
( P^3_3  is the number of permutation of 3 different items. However, since 2 items are the same (head & head), we need to divide by the factorial of the number of equal items, so  2! )

This gives us a probabilitiy of
 \frac{\frac{P^3_3}{2!}}{2^3}=\frac{3}{8}

Bunuel · Answer

No need to complicate. The only way Marco to loose $1 is for HHT scenario --> Marco's balance=-1-1+1=-1. This scenario can occur in 3!/2! ways (# of permutations of 3 letters HHT out of which 2 H's are identical).

As the total # of outcomes = 2^3 then P(HHT)=favorable/total=3/8.

lastshot · Answer

Its 3/8

Probability of individual event : 1/2 
No. of individual events : 3 therefore 1/2 X 1/2 X 1/2 = 1/8
No. of ways in which we can contain favorable result : 3 they are HTT, THT, TTH
thus 3X1/8 = 3/8

yamshi06 · Answer

probability of wining=1/2
probability of loosing=1/2

So,
1/2*1/2*1/2*3c2=3/8

vitorpteixeira · Answer

Bunuel

Should not be Total # of outcomes = 2^3 instead of 2^8 ??
Tks

Bunuel · Answer

Sure. It's 2^3 = 8 NOT 2^8 = 8. Edited. Thank you.

chaitanya1317 · Answer

Would appreciate help with this!

Does number of ways matter here? We are just concerned with the probability of Marco being -1$ and that's 1/8 right? 
I'm not clear about why we need to consider the other variations of HHT when we are dealing with a money situation.

Thanks!

krikre · Answer

Hi,

What is the approximate difficulty of this question on the 800 scale?

Thank you

BrentGMATPrepNow · Answer

I'd say around 600.

Cheers,
Brent

gurmukh · Answer

Marco will be $1 less when she has lost 2 chances and won 1 chances.
Possible cases for Marco
WLL + LWL + LLW
Every time Probability is 1/2×1/2×1/2 =1/8
Therefore answer is 3/8

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