An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?

• An experiment succeeds twice as often as it fails.
  
  i.e. the probability of its success is 2/3 and the probability of its failure is 1/3.
  
  In the next 5 trials the experiment needs to succeed in 4 out of the 5 trials.
  
  4 out of the 5 trials in which it succeeds could be selected in 5C4 ways = 5 ways.
  
  And as 4 of them are successes, they have a probability of 2/3 and the one that is a failure will have a probability of 1/3.
  
  Hence, the required probability = 5*((2/3)^4)*(1/3)
• 12 years agoHelpfull: Yes(33) No(1)
• according to bernoullis equation p(X=r)=ncr*p^r*q^n-r;
  p=probability of success,q=probability of fail=1-p;
  so here p=2q=2(1-p)=2-2p;
  p=2/3;q=1/3; 4 success probability=p(4)=5c4*(2/3)^4*(1/3)^1=5*16*1/3^5=80/243
• 13 years agoHelpfull: Yes(7) No(8)