Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Say you have 5 coins. 1 coin has heads on both sides and the [#permalink]

Show Tags

03 Nov 2009, 20:16

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

63% (01:45) correct
38% (00:52) wrong based on 2 sessions

HideShow timer Statistics

Say you have 5 coins. 1 coin has heads on both sides and the other 4 coins are normal (heads on one side, tails on the other)

A coin is selected at random and flipped five times, each time landing on heads. What is the probability that this coin is the coin that has heads on each side?

Say you have 5 coins. 1 coin has heads on both sides and the other 4 coins are normal (heads on one side, tails on the other)

A coin is selected at random and flipped five times, each time landing on heads. What is the probability that this coin is the coin that has heads on each side?

In this probability of \(\frac{9}{40}\) unfair coin contributed \(8\) shares out of \(9\), so the probability that the coin we chose randomly is unfair is: \(\frac{8}{9}\)
_________________

We determined that the probability of five heads is 8/40+1/40=9/40. So, there are 9 chances out of 40 this to happen.

But we know that this probability has already happened, so this 9 chances "worked". For this 9 chances unfair coin contributed 8 shares (8/40 of the probability) and fair coin only 1 (1/40). So the chance that the coin is unfair is 8 out of 8+1=9.

We can calculate this in another way as the probability P(h=5)=9/40, the chances that this is unfair coin would be (1/5)/(9/40)=8/9 and the probability that the coin is fair is (1/40)/(9/40)=1/9.

This problem is dealing with the concept of conditional probability which is advanced issue of probability. I doubt that much of this is needed for GMAT.

Would be nice to see OA and OE for this question.
_________________

There are five coins. Four of them are regular two-sided coins, and one of them has two Heads. (In other words, one of the coins has Heads on both sides.)

You pick a coin at random and flip it five times. It comes up Heads each time.

What is the probability that you picked the coin with two Heads (the coin with Heads on both sides)?

When a regular coin is flipped once it has a 1/2 chance of being heads. So for a regular coin to be heads five times it'll equal (1/2)^5 or 1/32 ... os one out of every 32 tries a coins will come up Heads fives times in a row.

We have 4 regular coins.. therefore 4 chances to hit the 5 heads with the regular coins...therefore 4*(1/32)= 1/8 probability that a regualr coin will be he 5 heads in a row.

Next we setup an equation. We know the probabilty of it hitting 5 heads in a row = 1 (it will happen) and we'll set X to be the probability that we selected the 2 headed coin.

so (1/8) + x = 1

therefore x=7/8

Answer: Probably that 2 headed coin picked was 7/8.

No idea if this is right, whats the OA?
_________________

There are five coins. Four of them are regular two-sided coins, and one of them has two Heads. (In other words, one of the coins has Heads on both sides.)

You pick a coin at random and flip it five times. It comes up Heads each time.

What is the probability that you picked the coin with two Heads (the coin with Heads on both sides)?

Probability of choosing any coin will be 1/5.

Probability of choosing the specific coin with two heads is (just one coin)/(lot of 5 coins) = 1/5.

Probability of choosing a normal coin with one head and one tail ( 4 of the remaining lot of 5 that are good coins)/(lot of 5 coins) = 4/5.

Here's how I look at it: 1/40 is the chance of picking up a non-trick coin and flipping 5H.

Chance of picking up a trick coin is 1/5, or 8/40.

Given that 5H has already happened, what is the probability that the coin is rigged?

Of all the times this event can occur, 8 of the 9 times would be due to a rigged coin. Only 1 of 9 chances would be attributed to pulling this off with a regular coin, if this event occurs.

Probability of choosing the specific coin with two heads is (just one coin)/(lot of 5 coins) = 1/5.

Probability of choosing a normal coin with one head and one tail ( 4 of the remaining lot of 5 that are good coins)/(lot of 5 coins) = 4/5.

That is all - PERIOD!!!

IMO, this would hold if all coins where equal. Given the outcome, 5 consecutive heads, not all the coins are equal.

they all have an equal chance of being selected but they DO NOT all have an equal chance of satisfying the 5H criteria.

The question is actually confusing.

It says pick a coin first. Then flip it five times and you get Heads everytime.

If you choose the bad coin, you are bound to get head everytime. So probability of getting a head with the bad coin is always 1 and probability of getting a tails is 0.

All you have got to do is pick the bad coin and the chances are 1/5. As you pick it, you will get five heads no matter what.

If the question was rephrased say, all coins are good with equal probability for a heads as 1/2 and tails as 1/2 as well, then the situation would change. You'd have to choose any one coin in 1/5 ways and then flip it 5 times to get 5 heads, for this you'd have to use the Bernoulli's trials concept. For the above situation as well, bernoulli's trials is applicable however, since probablity of getting heads is always 1, it ends up at 1/5.

Anyone with a better logic, I'd certainly appreciate it.
_________________

I dunno BarneyStinson, the way the question was worded seemed quite clear to me.

I also initially had trouble with it and (unfortunately) it took me more than 2 minutes to come up with the answer.

I drew a small probability tree as a visual guide. Obviously I didn't draw each flip, but only the whether the "desired" outcome us achieved (5H in a row).

The first coin has a probability of 1 of getting 5H if it is chosen, while it is 1/32 for the others. Next, I multiplied each probability by 1/5 (the chance of randomly choosing that coin). Finally, I divided 1/5 (1 multiplied by 1/5 - the "desired outcome") by (1/5 + 4/(32*5) - the total amount of outcomes) to get 8/9.

Conditional probability is a tricky concept, one thing good about it is that it's not tested in GMAT.

General case:

There are \(k\) coins: \(f\) are fair coins and \(c\) are counterfeit, two-headed coins (\(f+c=k\)). One coin is chosen at random and tossed \(n\) times. The results are all heads. What is the probability that the coin tossed is the two-headed one?

The probability that the coin tossed is two-headed: \(\frac{\frac{c}{k}*1^n}{\frac{f+c2^n}{k2^{n}}}=\frac{c2^n}{f+c2^n}\).

Now, if you substitute \(c\), \(f\) and \(n\) by the values from the original question you'll get the probability of \(\frac{8}{9}\).
_________________

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...