Probability-Tossing coins

Expert replies

ash4gmat: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Thu Sep 17, 2015 2:57 am

by ash4gmat » Fri May 06, 2016 11:29 pm

Is there any other method to solve this apart from listing down the options?

Urpi and Manco are playing a game where they flip a fair coin four times and try to predict the outcomes.

What is P(A), the probability that the second flip is heads?

What is P(B), the probability that the fourth flip is heads?

What is P(A and B), the probability that the second flip is heads and the fourth flip is heads?

Like this post

Source: Beat The GMAT — Problem Solving | Fri May 06, 2016 11:29 pm

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu May 12, 2016 12:45 am

Certainly!

For P(A), you have 2 * 2 * 2 * 2 = 16 total options. Your target is "Heads 2nd", for which there are 2 * 1 * 2 * 2 = 8 total options, giving you 8 / 16.

For P(B), same thing.

For P(A and B), you have 2 * 1 * 2 * 1 = 4 target options, for 1/4.

P(A and B) here = P(A) * P(B), so you could just do 1/2 * 1/2 as well.

Save $100 on any VP online course!

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu May 12, 2016 10:02 am

Hi ash4gmat,

As complex as this situation might seem, the 'math' behind it is rather simple. Coin flips are independent events - the result of one flip has NO impact on the results of any other flips. Thus, the probability of ANY flip being 'heads' is the same: 1/2.

These types of questions become more layered if you're asked to calculate a more complex outcome. The probability of flipping TWO heads on two tosses can be solve with a little table or a bit of math.

HH
HT
TH
TT

Here, there are only 4 possible outcomes with one of them matching what we're looking for. So the probability is 1/4. Mathematically, we can also solve it this way:

Probability of heads on the first flip: 1/2
Probability of heads on the second flip: 1/2
Probability of BOTH events occurring: (1/2)(1/2) = 1/4

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review