In a factory which manufactures bolts, machines A, B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?Marks:3
Let events B1, B2, B3
B1 = the bolt is manufactured by machine A
B2 = the bolt is manufactured by machine B
B3 = the bolt is manufactured by machine C
And E = ‘the bolt is defective’.
P(B1) = 0.25 P(E|B1) = 0.05
P(B2) = 0.35 P(E|B2) = 0.04
P(B3) = 0.40 P(E|B3) = 0.02
By Baye's theorem,
P(B1|E) = 0.05
Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag II.Marks:3
Let E1 = choosing the bag I, E2 = choosing the bag II and A = drawing a red ball.
If 2P(A) = P(B) = 5/13 and P(A|B) = 2/5, evaluate P(A B).Marks:1
P(AB) = P(A|B).P(B) = 2/5 x 5/13 = 2/13.
Now, P(AB) = P(A) + P(B) - P(AB)
P(AB) = 5/26 + 5/13 - 2/13 = 11/26.
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find P(AB).Marks:1
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(EF) = 0.2, find P (E|F) and P(F|E).Marks:1