Answer to Question #140760 in Statistics and Probability for navith

Question

A can solve 90 percent of the problems given in a book and B can solve 709 percent. what is the probability that at least one of them will solve a problem selected at random?

Answer 1

Let A and B be the events defined as follows :

$A$ be the event "A solves the problem", $B$ be the event "B solves the problem",

 $A$  and $B$  are independent events such that

$$P(A)=0.9, P(B)=0.7$$

The probability that at least one of them will solve a problem selected at random

$$P(A\cup B)=1-P(\bar{A})P(\bar{B})=$$

$$=1-(1-P(A))(1-P(B))=$$

$$=1-(1-0.9)(1-0.7)=0.97$$

Or

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

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

$$=0.9+0.7-0.9(0.7)=0.97$$