The occurrence of a disease in an industry is such that the workers have 20 % chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?

Step-by-step solution

aligned & Here, n =6 & p = P ( Suffering from disease )= 20 100 = 1 9 & q = P ( Not suffering from disease )=1- 1 5 = 4 5 & P ( x 4)= P ( x =4)+ P ( x =5)+ P ( x =6) & = ^6 c ₄ ( 1 5 )^4 ( 4 5 )^2+ ^6 c ₅ ( 1 5 )^5 ( 4 5 )^1+ ^6 c ₆ ( 1 5 )^6 & = 6! 4!2! 16 5^6 + 6! 5! 4 5^6 + 1 5^6 & = 1 (5)^6 [15 16+6 4+1] & = 240+24+1 15625 = 26.5 15625 = 53 3125 aligned