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Question Number 146927 by puissant last updated on 16/Jul/21

Answered by Olaf_Thorendsen last updated on 16/Jul/21

λ = ((P_V^− (M))/(P_V (M))) λ = ((P_V^− (M)P(V^− )P(V))/(P_V (M)P(V)P(V^− ))) λ = ((P_M (V^− )P(M)P(V))/(P_M (V)P(M)P(V^− ))) λ = ((P_M (V^− )P(V))/(P_M (V)P(V^− ))) λ = (((1−P_M (V))P(V))/(P_M (V)(1−P(V)))) Pour le vaccin A : λ_A = (((1−P_M (A))P(A))/(P_M (A)(1−P(A)))) λ_A = (((1−(8/(1000)))(1/4))/((8/(1000))(1−(1/4)))) = ((124)/3) ≈ 41,3 Pour le vaccin B : λ_B = (((1−P_M (B))P(B))/(P_M (B)(1−P(B)))) λ_B = (((1−(6/(1000)))(1/5))/((6/(1000))(1−(1/5)))) = ((497)/(12)) ≈ 41,4 Plus λ est grand et plus le vaccin est efficace : λ_A ≈ λ_B donc les deux vaccins B ont une efficacite comparable

$$\lambda\:=\:\frac{{P}_{\overset{−} {{V}}} \left({M}\right)}{{P}_{{V}} \left({M}\right)} \\ $$$$\lambda\:=\:\frac{{P}_{\overset{−} {{V}}} \left({M}\right){P}\left(\overset{−} {{V}}\right){P}\left({V}\right)}{{P}_{{V}} \left({M}\right){P}\left({V}\right){P}\left(\overset{−} {{V}}\right)} \\ $$$$\lambda\:=\:\frac{{P}_{{M}} \left(\overset{−} {{V}}\right){P}\left({M}\right){P}\left({V}\right)}{{P}_{{M}} \left({V}\right){P}\left({M}\right){P}\left(\overset{−} {{V}}\right)} \\ $$$$\lambda\:=\:\frac{{P}_{{M}} \left(\overset{−} {{V}}\right){P}\left({V}\right)}{{P}_{{M}} \left({V}\right){P}\left(\overset{−} {{V}}\right)} \\ $$$$\lambda\:=\:\frac{\left(\mathrm{1}−{P}_{{M}} \left({V}\right)\right){P}\left({V}\right)}{{P}_{{M}} \left({V}\right)\left(\mathrm{1}−{P}\left({V}\right)\right)} \\ $$$$ \\ $$$$\mathrm{Pour}\:\mathrm{le}\:\mathrm{vaccin}\:\mathrm{A}\:: \\ $$$$\lambda_{{A}} \:=\:\frac{\left(\mathrm{1}−{P}_{{M}} \left({A}\right)\right){P}\left({A}\right)}{{P}_{{M}} \left({A}\right)\left(\mathrm{1}−{P}\left({A}\right)\right)} \\ $$$$\lambda_{{A}} \:=\:\frac{\left(\mathrm{1}−\frac{\mathrm{8}}{\mathrm{1000}}\right)\frac{\mathrm{1}}{\mathrm{4}}}{\frac{\mathrm{8}}{\mathrm{1000}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}\right)}\:=\:\frac{\mathrm{124}}{\mathrm{3}}\:\approx\:\mathrm{41},\mathrm{3} \\ $$$$ \\ $$$$\mathrm{Pour}\:\mathrm{le}\:\mathrm{vaccin}\:\mathrm{B}\:: \\ $$$$\lambda_{{B}} \:=\:\frac{\left(\mathrm{1}−{P}_{{M}} \left({B}\right)\right){P}\left({B}\right)}{{P}_{{M}} \left({B}\right)\left(\mathrm{1}−{P}\left({B}\right)\right)} \\ $$$$\lambda_{{B}} \:=\:\frac{\left(\mathrm{1}−\frac{\mathrm{6}}{\mathrm{1000}}\right)\frac{\mathrm{1}}{\mathrm{5}}}{\frac{\mathrm{6}}{\mathrm{1000}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{5}}\right)}\:=\:\frac{\mathrm{497}}{\mathrm{12}}\:\approx\:\mathrm{41},\mathrm{4} \\ $$$$ \\ $$$$\mathrm{Plus}\:\lambda\:\mathrm{est}\:\mathrm{grand}\:\mathrm{et}\:\mathrm{plus}\:\mathrm{le}\:\mathrm{vaccin}\:\mathrm{est} \\ $$$$\mathrm{efficace}\:: \\ $$$$ \\ $$$$\lambda_{{A}} \:\approx\:\lambda_{{B}} \:\mathrm{donc}\:\mathrm{les}\:\mathrm{deux}\:\mathrm{vaccins}\:\mathrm{B}\:\mathrm{ont}\:\mathrm{une} \\ $$$$\mathrm{efficacite}\:\mathrm{comparable} \\ $$

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