Problem87: Probability

¡Puedes leer este texto en español! Problema87: Probabilidad

Ej87. A company makes a quality control to each batch of 16 engines. In the quality control, 2 engines are randomly selected (without replacement) of each batch of 16 engines and they are inspected.

If any of the two is defective, all the batch will be rejected but if none is defective, the 16 engines will be accepted and they will send for sell.

If it is inspected a batch of 16 engines which only has one defective, calculate the probability that the batch is rejected .


We perform a data compilation given by the problem statement

· It will randomly select two engines (without replacement) from a total of 16.
· It assumes that the engines are independent: P(X_n ∩ X_m) = 0
· X_i ≡ 'Defective i-Engine'.

· P(X_i) = 1/16.

We have to get the following probability:

P(X₁ ∪ X₂) = P(X₁) + P(X₂) = 1/16 + 1/16 = 1/8

So, the probability that the batch will be rejected (any of the engines is defective) is 0.125.