It is given that the probability that A can solve a given problem is $\frac{3}{5}$ and the probability that B can solve the same problem is $\frac{2}{3}$. The probability that at least one of A and B can solve a problem isA. $\frac{2}{5}$B. $\frac{1}{15}$C. $\frac{13}{15}$D. $\frac{2}{15}$

Home » It is given that the probability that A can solve a given problem is and the probability that B can solve the same problem is . The probability that at least one of A and B can solve a problem isA. B. C. D.

It is given that the probability that A can solve a given problem is $\frac{3}{5}$ and the probability that B can solve the same problem is $\frac{2}{3}$ . The probability that at least one of A and B can solve a problem is
A. $\frac{2}{5}$
B. $\frac{1}{15}$
C. $\frac{13}{15}$
D. $\frac{2}{15}$

It is given that the probability that A can solve a given problem is $\frac{3}{5}$ and the probability that B can solve the same problem is $\frac{2}{3}$ . The probability that at least one of A and B can solve a problem is
A. $\frac{2}{5}$
B. $\frac{1}{15}$
C. $\frac{13}{15}$
D. $\frac{2}{15}$

$\mathrm{P}(\mathrm{A})=$ probability that A can solve the problem
$=3 / 5$
And $P(B)=$ probability that $B$ can solve the problem $=2 / 3$
$P(A \cup B)=P(A)+P(B)$ , As the events are independent
$\Rightarrow P(A \cap B)=P(A) \cdot P(B)$
Thus,
$\Rightarrow \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})=3 / 5+2 / 3-2 / 5=13 / 15$
Hence, correct option is c.