Answer to Question #194230 in Statistics and Probability for khunyeledzo

Question

A shipment of 100 bags of sugar is rumoured to have some bags that contain illegal drugs. Local customs officials decided to screen shipment by randomly testing 4 bags. If any are found to contain drugs, the whole consignment is sized.

Compute the probability that the shipment consisting of 95 bags of sugar and 5 bags of illegal drugs will be detected in this manner

Answer 1

$P(X>0)=1-P(X=0)=1-\frac{95}{100}*\frac{94}{99}*\frac{93}{98}*\frac{92}{97}=0.1881.$