A , B, C try to hit a target simultaneously b | vedclass

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Question

$P(	ext { A or } B 	ext { but not by } C)=P((A \cup B) \cap \bar{C})$

$=P(A \cup B) 	imes P(\bar{C})$

$=[\mathrm{P}(\mathrm{A})+\mathrm{P}(\m

Vedclass · Accepted Answer

$21/64$

Vedclass · Answer

$P(	ext { A or } B 	ext { but not by } C)=P((A \cup B) \cap \bar{C})$

$=P(A \cup B) 	imes P(\bar{C})$

$=[\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})] 	imes \mathrm{P}(\overline{\mathrm{C}})$

$=$ $\left[\frac{3}{4}+\frac{1}{2}-\frac{3}{4} 	imes \frac{1}{2}ight] 	imes \frac{3}{8}=\left(\frac{6+4-3}{8}ight) 	imes \frac{3}{8}=\frac{21}{64}$

$A , B, C$ try to hit a target simultaneously but independently. Their respective probabilities of hitting targets are $\frac{3}{4},\frac{1}{2},\frac{5}{8}$. The probability that the target is hit by $A$ or $B$ but not by $C$ is

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