Sign Up FREE!  Sign In  Classroom Setup  Common Core Alignment  


Thread Tools  Display Modes 
07262007  #1 
Guest
Posts: n/a

A coin is tossed five times. Find the probability of getting exactly three heads.?
A coin is tossed five times. Find the probability of getting exactly three heads.?

07262007  #2 
Guest
Posts: n/a

You have to get three heads and two tails, and there is more than one way of doing this. The formula isp(3) = 5C3 Ã— 0.5^3 Ã— 0.5^2where 5C3 = 5!/3!2! = 10 is the number of ways of selecting 3 things out of 5.This gives the probability of exactly three heads as 0.3125..

07262007  #3 
Guest
Posts: n/a

The probability of getting a head in each toss is 1/2. Similarly the probability of getting a tail is also 1/2. The probability distribution is binomial.(H + T)^5 and the coefficient of the term H^3 will be the probability.

07262007  #4 
Guest
Posts: n/a

The probability is always 50  50. Chance confounds the law of averages because each flip is individual, each rotation of the coin will be unlike the previous or the next flip. It is just as likely to produce five "heads" as five "tails". Unless, of course, you know what you're doing. But that's a route that eliminates chance.

07262007  #5 
Guest
Posts: n/a

Tougher than it looks. Here we go:Flip a coin. You get H (heads) or T (tails). So two possible outcomes in one flip. If you flip it 5 times, you have 2^5=32 possible outcomes.How many of these 32 outcomes contain exactly 3 heads?When we have three heads, we must also have exactly three tails, so your goal is to determine how many combinations of this there are. Consider one option:HHHTTFirst we need to flip three heads in a row. The odds of this happening are (1/2)^3=1/8Then we need to flip two tails in a row. Odds: (1/2)^2=1/4. So the probability of getting HHHTT is (1/8)(1/4)=1/32 (good general idea to remember in probability problems: x=and, +=or).Now consider another option: HHTHT. We flip 2 heads (odds: (1/2)^2=1/4), 1 tails (odds: 1/2), 1 heads (1/2), and another tails (1/2). So the odds of getting this combination are (1/4)(1/2)(1/2)(1/2)=1/32.The point is, the probability of getting each combination of 3 H's and 2 T's is always the same, 1/32. So, how many possible 5 flip combinations have 3 heads? Well, that would be solved as a combination, 5C3=5!/(3!2!)=10. So the answer is 10(1/32)=10/32=5/16

07262007  #6 
Guest
Posts: n/a

Flip a coin. You get H (heads) or T (tails). So two possible outcomes in one flip. If you flip it 5 times, you have 2^5=32 possible outcomes.How many of these 32 outcomes contain exactly 3 heads?When we have three heads, we must also have exactly three tails, so your goal is to determine how many combinations of this there are. Consider one option:HHHTTFirst we need to flip three heads in a row. The odds of this happening are (1/2)^3=1/8Then we need to flip two tails in a row. Odds: (1/2)^2=1/4. So the probability of getting HHHTT is (1/8)(1/4)=1/32 (good general idea to remember in probability problems: x=and, +=or).Now consider another option: HHTHT. We flip 2 heads (odds: (1/2)^2=1/4), 1 tails (odds: 1/2), 1 heads (1/2), and another tails (1/2). So the odds of getting this combination are (1/4)(1/2)(1/2)(1/2)=1/32.The point is, the probability of getting each combination of 3 H's and 2 T's is always the same, 1/32. So, how many possible 5 flip combinations have 3 heads? Well, that would be solved as a combination, 5C3=5!/(3!2!)=10. So the answer is 10(1/32)=10/32=5/16 this is wat my teacher said.

05162015  #7  
Join Date: May 2015
Posts: 135
Thanks: 2,360
Thanked 825 Times in 121 Posts

guests please read please register its completely free no money involved so Hit that register button with your face :3
__________________
IM BACK AND ITS TIME FOR SOME FUN YAAAAAAAAAAY Last edited by naruto beast; 06102015 at 07:10 AM.. 

The Following 3 Users Say Thank You to naruto beast For This Useful Post: 
05162015  #8  
Join Date: May 2015
Posts: 135
Thanks: 2,360
Thanked 825 Times in 121 Posts

come on guys
really register!
__________________
IM BACK AND ITS TIME FOR SOME FUN YAAAAAAAAAAY 

The Following 3 Users Say Thank You to naruto beast For This Useful Post: 
05192015  #9  
Join Date: Dec 2011
Posts: 386
Thanks: 1,476
Thanked 1,457 Times in 446 Posts

Ya man.
__________________
Finally finished all my tests!!! I am ekko main now ^_^ (ign: supersaiyan2363) It's not how much time you have, it's how you use it. Ekko 

The Following User Says Thank You to Dragonballful23 For This Useful Post:  Joe1239012390 (10192015) 
Thread Tools  
Display Modes  

