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

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P""(AuuB) is (1) 3/5 (2) 0 (3) 1 (4) 2/5

If A and B are two events such that P(A)=(4)/(7), P(AnnB)=(3)/(28) and the conditional probability P((A)/(A^(c )uuB^(c ))) (where A^(c ) denotes the compliment of the event A) is equal to lambda , then the value of (26)/(lambda) is equal to

Let A & B be two events. Suppose P(A) = 0.4 , P(B) = p and P(AuuB)=0.7 The value of p for which A and B are independent is

If A and B are exhaustive events in a sample space such that probabilites of the events AnnB , A , B and AuuB are in A.P. If P(A)=K , where 0 lt K le 1 , then

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.

Let the equation of the circle is x^(2) + y^(2) - 2x-4y + 1 = 0 A line through P(alpha, -1) is drawn which intersect the given circle at the point A and B. if PA PB has the minimum value then the value of alpha is.

Let P denotes the plane consisting of all points that are equidistant from the points A(-4,2,1) and B(2,-4,3) and Q be the plane, x-y+cz=1 where c in R . If the angle between the planes P and Q is 45^(@) then the product of all possible values of c 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 computers produced in the factory turn out to be defective. It is known that P(computer turns out to bedefective, given that it is produced in plant T_(1) )=10P (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

For the three events A , B and C , P (exactly one of the events A or B occurs) = P (exactly one of the events B or C occurs) =P (exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p^2 , where 0ltplt1/2 . Then, find the probability of occurrence of at least one of the events A , B and C .

For the three events A ,B , and C , P (exactly one of the events A or B occurs)= P (exactly one of the two evens B or C )= P (exactly one of the events C or A occurs)= p and P (all the three events occur simultaneously)= p^2 where 0 < p < 1//2 . Then the probability of at least one of the three events A , B and C occurring is