Question

If E and F be two events such that P(E) = 1/3, P(F) = 1/4, find P(E U F) if E and F are independent events.

Show that the function f(x) = x³ – 3x² + 6x – 100 is increasing on R.

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.

If E and F are independent events, then show that (i) E and F' are independent events. (ii) E' and F are also independent events.

Find : $\textstyle\int$${\frac{\left(x^{4}-x\right)^{\frac{1}{4}}}{x^{5}}}\,.$

A box contains 50 bolts and 50 nuts. Half of the bolts and nuts are rusted. If two items are drawn with replacement, what is the probability that either both are rusted or both are bolts.

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)