## Statistics for the Life Sciences (5th Edition)

P(X=j) = $\frac{n!}{j!(n-j)!}$$p^{j}$$(1-p)^{n-j}$
a.) P(all 20 will be cured) = $\frac{20!}{20!0!}$$0.9^{20}$$(1-0.9)^{0}$ = 0.1216 b.) P(all but 1 will be cured) = $\frac{20!}{19!1!}$$0.9^{19}$$(1-0.9)^{1}$ = 0.2702 c.) P(exactly 18 will be cured) = $\frac{20!}{18!2!}$$0.9^{18}$$(1-0.9)^{2}$ = 0.2852 d.) 90% of 20 = 18 P(exactly 90% will be cured) = P(exactly 18 will be cured) P(exactly 90% will be cured) = $\frac{20!}{18!2!}$$0.9^{18}$$(1-0.9)^{2}$ = 0.2852