My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum

Thanks Tree1Thanks
  • 1 Post By Olinguito
LinkBack Thread Tools Display Modes
April 9th, 2014, 07:00 PM   #1
Senior Member
Joined: Jan 2009

Posts: 345
Thanks: 3

How many sequences contain 2 Tails and 3 Heads

Confused about this one.
I flip a coin 5 times. How many sequences have 2 tails and 3 heads?
Is it Binomial[5,2]+Binomial[5,3] = 20?
sivela is offline  
April 9th, 2014, 11:32 PM   #2
Senior Member
Joined: Apr 2014
From: UK

Posts: 965
Thanks: 342

I used finger-maths and added them up manually.
these are the sequences with 2 tails
1,2 1,3 1,4 1,5 2,3 2,4 2,5 3,4 3,5 4,5
So the answer is 10
This is probably your Binomial[5,2].
The other half isn't required as it's implied, with 2 tails the other 3 must be heads anyway
weirddave is offline  
April 10th, 2014, 12:04 AM   #3
Senior Member
Olinguito's Avatar
Joined: Apr 2014
From: Greater London, England, UK

Posts: 320
Thanks: 156

Math Focus: Abstract algebra
As there are only a handful of possibilities, we can list them all exhaustively:














So there are $10$ possibilities.

In general if a coin is thrown $n$ times, any sequence with exactly $r$ tails with have exactly $n-r$ heads and vice versa. So to find the number of sequences with exactly $r$ tails, compute EITHER $^n\mathrm C_r$ (tails) OR $^n\mathrm C_{n-r}$ (heads).
Thanks from sivela
Olinguito is offline  

  My Math Forum > College Math Forum > Advanced Statistics

binomial, heads, sequences, tails

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Probability of getting an even number of tails for x throws? Kuroniirp Probability and Statistics 6 October 6th, 2013 05:23 PM
Effects of Clustering of Heads or Tails coolcat Advanced Statistics 1 November 27th, 2011 11:03 PM
Maximize the thinking power of dragon heads darandoma Algebra 3 September 22nd, 2011 10:35 PM
Probabilty of consecutive heads/tails in weighted coin toss slyone Algebra 2 September 5th, 2008 04:05 PM
Probabilty of consecutive heads/tails in weighted coin toss slyone Advanced Statistics 1 September 4th, 2008 06:13 AM

Copyright © 2019 My Math Forum. All rights reserved.