An electric component manufactured by`'RASU` electronics' is tested for its defectiveness by asophisticated testing device. Let A denote the event the device is defective and B the event thetesting device reveals the component to be defective. Suppose `P(A) = a. 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

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

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 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

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 following is not correct ?

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

If A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta, sin 2beta] , [sin 2 beta, -cos2beta]] where 0 lt beta lt pi/2 then prove that BAB=A^(-1) Also find the least positive value of alpha for which BA^4B= A^(-1)

Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where k is some unknown constant. P(X=x)={{:(0.1, "if "x =0),(kx, "if "x = 1 or 2 ),(k(5-x), "if " x=3 or 4),(0,"otherwise"):} (a) Find the value of k. (b) What is the probability that you study at least two hours ? Exactly two hours? At most two hours?

Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0,alphaa n d1//beta are the roots of the equation a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot Statement 1: (p^2-q)(b^2-a c)geq0 Statement 2: b!=p aorc!=q a

Statement-1: if A and B are two events, such that 0 lt P(A),P(B) lt 1, then P((A)/(overline(B)))+P((overline(A))/(overline(B)))=(3)/(2) Statement-2: If A and B are two events, such that 0 lt P(A), P(B) lt 1, then P(A//B)=(P(AcapB))/(P(B)) and P(overline(B))=P(A capoverline(B))+P(overline(A) cap overline(B))