Question

Prove that if E and F are independent events, then the events E and F' are also independent.

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then find P(A/B).

If A = $\left(\begin{array}{l l }3 & 1 \\ -1 & 2\end{array}\right)$ and I = $\left(\begin{array}{l l }1 & 0 \\ 0 & 1\end{array}\right)$ find k so that A² = 5A + kI.

From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.

If A and B are two independent events, then prove that the probability of occurrence of at least one of A and B is given by 1 – P(A’) · P(B’)

Find the angle between the vectors ${\vec{a}}={\hat{i}}+{\hat{j}}-{\hat{k}}$ and ${\vec{b}}={\hat{i}}-{\hat{j}}+{\hat{k}}$

If P(E) = 6/11, P(F) = 5/11 and P(E ∪ F) = 7/11 then find (i) P(E/F) (ii) P(F/E)