Ten eggs are drawn successively will replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.
Abag contains 4 red and 4 black balls. Another bag contains 2 red and 6 black balls. One of two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
Find the equation of the plane which contains the line of intersection of the planes $\vec{r} \cdot(\hat{i}+2 \hat{j}+3 \hat{k})-4=0, \quad \vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})+5=0$ and which is perpendicular to the plane $\vec{r} \cdot(5 \hat{i}+3 \hat{j}-6 \hat{k})+8=0$.