40 microwave ovens were shipped to an appliance store, 3 of the 40 were defective. What is the probability that exactly 2 of the first 4 sold are defective?

Answer 1

what is the probability that exactly 2 of the 1st 4 sold are defective, if 3 of 40 are defective?

ways 2 of 4 are defective are

DDNN

DNDN

DNND

NDDN

NDND

NNDD

6 ways 4P2 = 4!/2! = 4x3/2 = 12/2 = 6

P(DDNN) = 3/40 x 2/39 x 37/38 x 36/37

P(DNDN) = 3/40 x 37/39 x 2/38 x 36/37

P(DNND) = 3/40 x 37/39 x 36/38 x 2/37

notice they all have the same 4 factors in the numerator and the same 4 in the denominator

for all 6 ways

sum them = 6x the products of the numerators over the products of the denominators: 3x2x37x36/37x38x39x40 =6x 6x36/38x39x40 = 18x9/19x10x39 = 27/19x5x13 = 27/248x5

= 27/1240 = Probability of exactly 2 defective in the 1st 4 sold