Question

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

Answer 1

sample space =12
favourable conditions =9
P(E)=9/12=3/4=0.74

Answer 2

Hey !!

Let p be the probability of success

p = 10% = 10/100 = 1/10

and $q = 1 - \frac{1}{10} = \frac{9}{10} , n = 12$

Now, The probability of getting r successes is given by

P (X = r) = ¹²Cr(9/10)¹²⁻^r.(1/10)^r where r = 0, 1 , 2 ,....., 12

P (X = 9) = ¹²C₉(9/10)³.(1/10)⁹

          = 220 × (9)³/(10)¹²

          = 22 × (9)³ / (10)¹¹

GOOD LUCK !!