supposed 100 refrigerator were manufactured during a day. ninety five operated perfectly and 5 had atleast one defect. a sample of four is selected at random. using the hypergeometric distribution formula, find the probability that 8 of the 10 will operate perfectly?

Solution:

• K is the number of successes in the population, K=95
• k is the number of observed successes,k=8
• N is the population size, N=100
• n is the number of draws, n=10

$P(X=k)=\dfrac{^KC_k\times ^{N-K}C_{n-k}}{^NC_n} \\ P(X=8)=\dfrac{^{95}C_8\times ^{100-95}C_{10-8}}{^{100}C_{10}} \\=\dfrac{^{95}C_8\times ^{5}C_{2}}{^{100}C_{10}} \\=0.0702$