<p>Of all the articles in a box, 80% are satisfactory, while 20% are not. The probability of obtaining exactly five good items out of eight randomly selected articles is
a)0.800
b) 0.003
c) 0.147
d) 0.013
e) 0.132</p>
<p>Answer is C, but i have no idea how to get this</p>
<p>Start with a simpler version of the problem: what's the probability that the first 5 you pick will be S (=Satisfactory), and that the next 3 will be N (=not satisfactory)? This probability is ((0.8)^5) ((0.2)^3) = 0.00262 .</p>
<p>However, this is just <em>one</em> of the several combinations of (5S, 3N) possible; you need to multiply this by the # of such combinations. This number is 8C3 = (8)(7)(6)/ (3)(2)(1) = 56. The final answer is
(0.00262)(56) = 0.1468 .</p>
<p>[If you still have trouble understanding this, try a smaller version of the problem: what's the probability of getting exactly two good items out of four selected? If you actually write out all the possible results of picking 4 items, you get 16 possibilities:</p>
<p>NNNN : probability = (0.2)^4
NNNS
NNSN
NNSS
NSNN
NSNS
NSSN
NSSS
SNNN
SNNS
SNSN
SNSS
SSNN
SSNS
SSSN
SSSS : probability = (0.8)^4</p>
<p>Of these 16 possible outcomes, how many have exactly 2 S's? There are six of them; you can compute the probability of each (will be (0.8)(0.8)(0.2)(0.2)) and add these probabilities to get (6)(0.0256) as the final answer to this smaller problem. ]</p>