A factory has 3 machines A₁, A₂, A₃ producing 1000, 2000, 3000 bolts per day respectively. A₁ produces 1% defectives, A₂ produces 1.5% and A₃ produces 2% defectives. A bolt is chosen at random and found defective. What is the probability that it comes from machine A₁?

Find the Quartile deviation.

Wages (Rs)	20-30	30-40	40-50	50-60	60-70
No. of labourers	3	5	20	10	5

Two identical boxes containing respectively 4 white and 3 red balls, 3 white and 7 red balls. A box is chosen at random and a ball is drawn from it. Find the probability that the ball is white. If the ball is white. If the ball is white, what is the probability that it is from first box?

Three events A, B and C have probabilities \(\frac { 2 }{ 5 } ,\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 2 } \)  respectively. Given that \(P(A\cap C)=\frac { 1 }{ 5 } \) and \(P(B\cap C)=\frac { 1 }{ 4 } ,\)find P(C/B) and \(P(\bar { A } \cap \bar { C } )\)

Two dice are thrown together. Let A be the event "getting 6 on the first die" and B be the event "getting 2 on the second die". Are the events A and B independent?