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Question Number 182695 by cortano1 last updated on 13/Dec/22

$$\mathrm{If}\mathrm{two}\mathrm{events}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}\mathrm{such}$$$$\mathrm{that}\mathrm{P}\left({\mathrm{A}}^{\mathrm{c}}\right)=0.3;\mathrm{P}\left(\mathrm{B}\right)=0.4\mathrm{and}$$$$\mathrm{P}(\mathrm{A}\cap {\mathrm{B}}^{\mathrm{c}})=0.5\mathrm{then}\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}\cup {\mathrm{B}}^{\mathrm{c}}}\right)=?$$$$\left(\mathrm{A}\right)0.20\left(\mathrm{B}\right)0.25\left(\mathrm{C}\right)0.30\left(\mathrm{D}\right)0.35$$$$$$

Commented by Acem last updated on 13/Dec/22

$$Hifriend!$$$$WhatdoesA{}^{c}mean?$$

Commented by Emrice last updated on 13/Dec/22

$$$$it is the conditional probability. and in our case here it is the probability of A knowing C.

Answered by greougoury555 last updated on 14/Dec/22

$$P(B/A\cup \bar{B})=\frac{P(A\cap B)}{P(A\cup \bar{B})}$$$$=\frac{0.7-0.5}{0.7+0.6-0.5}=\frac{0.2}{0.8}=0.25$$

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