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Question Number 145869 by Ar Brandon last updated on 09/Jul/21

$$\mathrm{Let}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{be}2\mathrm{events}\mathrm{such}\mathrm{that}\mathrm{P}\left(\mathrm{A}\right)=0.4,\mathrm{P}\left(\stackrel{-}{\mathrm{B}}/\mathrm{A}\right)=0.7$$$$\mathrm{and}\mathrm{P}\left(\mathrm{B}/\stackrel{-}{\mathrm{A}}\right)=0.6,\mathrm{then}\mathrm{find}$$$$\left(i\right)\mathrm{P}\left(\stackrel{-}{\mathrm{B}}/\stackrel{-}{\mathrm{A}}\right)\left(ii\right)\mathrm{P}(\mathrm{A}\cap \mathrm{B})\left(iii\right)\mathrm{P}\left(\mathrm{B}\right)\left(iv\right)\mathrm{P}(\mathrm{A}\cup \mathrm{B})$$

Answered by gsk2684 last updated on 09/Jul/21

$$usingmultiplicationtheorem$$$$P(A\cap \stackrel{-}{B})=0.4\times 0.7$$$$\Rightarrow P\left(A\right)-P(A\cap B)=0.28$$$$\Rightarrow P(A\cap B)=0.4-0.28=0.12$$$$\mathrm{\&}P(B\cap \stackrel{-}{A})=0.6\times 0.6$$$$\Rightarrow P\left(B\right)-P(B\cap A)=0.36$$$$\Rightarrow P\left(B\right)=0.36+0.12=0.48$$$$proceedwiththese$$$$$$

Commented by Ar Brandon last updated on 09/Jul/21

$$\mathrm{Thank}\mathrm{you}\mathrm{Sir}$$

Answered by bramlexs22 last updated on 09/Jul/21

Commented by Ar Brandon last updated on 09/Jul/21

$$\mathrm{Thank}\mathrm{you}\mathrm{Sir}$$

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