Answer to Question #259225 in Statistics and Probability for Lala

Question

X can solve 80% of the problems while Y can solve 90% of the problems given in a statistics book. A problem is selected at random. What is the probability that at least one of them will solve the same?

Answer 1

Let $p(X)$ be the probability that that individual $X$ solves the problem and $p(Y)$ be the probability that individual $Y$ solves the problem. These probabilities are given as,

$p(X)=0.80$

$p(Y)=0.90$

Since the event that individual X solves the problem is independent of the event that individual Y solves the problem, then the probability  that at least one of them will solve the problem is given as,

$p(at\space least\space one\space solves\space the \space problem)=1-(p(X')*p(Y'))$

Now,

$p(X')=1-p(X)=1-0.8=0.2$ and $p(Y')=1-p(Y)=1-0.90=0.1$

The probability that at least one of them solve is,

p(at least one solves the problem)=1-(0.2*0.1)=1-0.02=0.98

Thus, the probability that at least one of them will solve the same is 0.98.