Using  C(n,r) = n!/((n-r)!r!)   below...





There are  outcomes possible.  So 8 will be the denominator.



How many outcomes have 0 heads?   1   (TTT)



How many outcomes have 1 head?  C(3,1) = 3    (HTT, THT, TTH)



How many outcomes have 2 heads?  C(3,2) = 3    (HHT, HTH, THH)



How many outcomes have 3 heads?  C(3,3) = 1    (HHH)





Thus the distribution is:

  0 heads:   1/8

  1 head:    3/8

  2 heads:   3/8

  3 heads:   1/8



(Note they sum to 8/8 = 1, which is expected since one of these outcomes must occur)



The function notation is   P(r heads) =  ,  



 

Answer by ikleyn(52931)   (Show Source): You can put this solution on YOUR website!
 .

find the probability distribution and distribution function 

for the numbers of head when 3 balanced coins are tossed

~~~~~~~~~~~~~~~~~~~~~~~~~~~







These words  " probability distribution "  and  " distribution function "  mean the same:



they denote the same conception.   In other words,  they are synonyms.





Therefore, in your post there is no need to ask twice about the same thing.



To ask once is just quite enough.







Being too pathetic doesn't make your post better. 



Asking twice, you demonstrate lack of knowledge on the subject.







 

RELATED QUESTIONS

If 4 balanced coins are tossed simultaneously (or 1 balanced coin is tossed 4 times),... (answered by Boreal)

Obtain a probability distribution for the number of heads when three coins are tossed. ?
 (answered by Boreal)

Obtain a probability distribution for the number of heads when 3 coins are tossed. Also... (answered by Fombitz)

Let X be the number of tails that turned up when two fair coins are tossed. What are the... (answered by ikleyn)

Find the probability of seeing exactly one head when 4 fair coins are... (answered by stanbon)

	What is the Probability of obtaining at least one head when 4 coins are tossed... (answered by Theo)

A coin is biased so that a head is twice likely as a head. 
If the coin is tossed three... (answered by stanbon)

from a box 6 dimes and 3 nickles, 4 coins are selected at a random with replacement.find... (answered by robertb)

Four coins are tossed. Find the probability of tossing at least one head.  (answered by Edwin McCravy,ikleyn)