Question

If P(A) = 0.4, P(B) = p, P(A U B) = 0.6 and A and B are given to the independent events, find the value of ‘p’.

If P(E) = 7/13, P(F) = 9/3 and P(E' / F') = 4/3, then evaluate : (i) P(E / F) (ii) P(E / F)

Verify that ax² + by² = 1 is a solution of differential equation $x(y y_{2}+y_{1}^{2})=y y_{1}.$

Find the sum of the order and the degree of the following differential equations : ${\frac{d^{2}y}{d x^{2}}}+{3{\sqrt\frac{{d y}}{d x}}}+(1+x)=0$

If P(F) = 0·35 and P(E U F) = 0·85 and E and F are independent events. Find P(E).

Obtain the differential equation of the family of circles passing through the points (a, 0) and (– a, 0).

Find the area of the parallelogram whose diagonals are represented by the vectors $\stackrel{\rightarrow}{a}\$ = $2{\hat{i}}-3{\hat{j}}+4{\hat{k}}$ and ${\vec{b}}=2{\hat{i}}-{\hat{j}}+2{\hat{k}}$