Question

From a lot of $10$ items containing $3$ defectives, a sample of $4$ items is drawn at random without replacement. The expected number of defective items is

• A. $3$
• B. $1.8$
• C. $1.2$
• D. $2.8$

Answer 1

The correct option is C $1.2$

P(1 Defective) $=C(3,1)\ast C(7,3)/C(10,4)=105/210=1/2$
P(2 Defective) $=C(3,2)\ast C(7,2)/C(10,4)=63/210=3/10$
P(3 Defective) $=C(3,3)\ast C(7,1)/C(10,4)=7/210=1/30$
P(4 Defective) $=0$
Avg value $=1\ast 1/2+2\ast 3/10+3\ast 1/30+4\ast 0+0\ast P\left(0defective\right)=1.2$