Answer to Question #267517 in Statistics and Probability for girlenigma

Question

Two drones are used to deliver parcels in succession. The probability of each drone correctly delivering the parcel assigned to it is 0.3 and 0.2 respectively. Find the probability that the parcel is delivered

Answer 1

Let $A$ denote the event "first drone delivers the parcel correctly".

Let $B$ denote the event "second drone delivers the parcel correctly".

Given $P(A)=0.3, P(B)=0.2.$ Since the events are independent, then

$$P(A\cap B)=P(A)P(B)$$

Find the probability that the parcel is delivered

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

$$=P(A)+P(B)-P(A)P(B)$$

$$=0.3+0.2-0.3(0.2)=0.44$$