Question

$n$ is an integer chosen at random from the set $\{2,5,6\}$ and $p$ another integer chosen at random from the set $\{6,9,10\}$. What is the probability that the two numbers $n$ and $p$ are even?

• A. $\frac{2}{9}$
• B. $\frac{5}{9}$
• C. $\frac{4}{9}$
• D. $\frac{1}{9}$

Answer 1

Answer: (C)

$\frac{4}{9}$

Total number of elements in $setS1\{2,5,6\}=3$

Total number of elements in $setS2\{6,9,10\}=3$

Number of element that are even in set $S1=2$

Number of element that are even in set $S2=2$

$P\left(A\right)=\frac{Numberoffavourableoutcomes}{TotalNumberofpossibleoutcomes}$

$P\left(A\right)=P\left(S1\right)\times P\left(S2\right)$

$\therefore P\left(A\right)=\frac{2}{3}\times \frac{2}{3}=\frac{4}{9}$

hence, option $C$ is correct.