An electric component manufactured by`'RASU` electronics' is tested for its defectiveness by a sophisticated testing device. Let A denote the event the device is defective and B the event the testing device reveals the component to be defective. Suppose `P(A) = alpha`. and `P((B)/(A))= P((B')/(A'))= 1- alpha,` where `0 lt alpha lt1.` If the probability that the component is not defective is `lambda.` then the value of `4lambda` is

A computer producing factory has only two plants T_(1) and T_(2). Plant T_(1) produces 20% and plant T_(2) produces 80% of the total computers produced . 7% of the computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective givent that it is produced in plant T_(1)) = 10 P ( computer turns out to be defective given that it is produced in plant T_(2)), where P (E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T_(2) is

Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside O A B which satisfy d(P , O A)lt=min[d(p ,O B),d(P ,A B)] , where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.

If A and B are independent events such that 0 lt P (A) lt 1 and 0 lt P (B) lt 1 then which of the followingis not correct ?

Through the point P(alpha,beta) , where alphabeta>0, the straight line x/a+y/b=1 is drawn so as to form a triangle of area S with the axes. If a b >0, then the least value of S is

The circle x^2+y^2=4 cuts the line joining the points A(1, 0) and B(3, 4) in two points P and Q . Let (BP)/(PA)=alpha and (BQ)/(QA)=beta . Then alpha and beta are roots of the quadratic equation

A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having its foci as S_1 and S_2 . If the internal angle bisector of the angle angleS_1PS_2 cuts the x-axis at poin Q(alpha, 0) then range of alpha is

Let A and B be two events, such that P(bar(A cup B))=(1)/(6), P(A cap B)=(1)/(4) and P(barA)=(1)/(4) , where barA stands for complement of event A. Then events A and B are :

If the tangent to the curve y = 1 – x^(2) at x = alpha , where 0 lt alpha lt 1, meets the axes at P and Q. Also alpha varies, the minimum value of the area of the triangle OPQ is k times area bounded by the axes and the part of the curve for which 0 lt x lt 1 , then k is equal to

Let A and B be two events such that Poverline((AcupB))=(1)/(6),P(AcapB)=(1)/(4) and Poverline(A)=(1)/(4) ,where overline(A) stands for complement of event A. then , events A and B are