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Question

$A:$ Event when card $A$ is drawn

$\mathrm{B}:$ Event when card $\mathrm{B}$ is drawn.

$\mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})=\frac{1}{2

Vedclass · Accepted Answer

$\frac{11}{16}$

Vedclass · Answer

$A:$ Event when card $A$ is drawn

$\mathrm{B}:$ Event when card $\mathrm{B}$ is drawn.

$\mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})=\frac{1}{2}$

Required probability $=\mathrm{P}(\mathrm{AA} 	ext { or }(\mathrm{AB}) \mathrm{A}$

or $(\mathrm{BA}) \mathrm{A} 	ext { or }(\mathrm{ABB}) \mathrm{A} 	ext { or }(\mathrm{BAB}) \mathrm{A} 	ext { or }(\mathrm{BBA}) \mathrm{A})$

$=\frac{1}{2} 	imes \frac{1}{2}+\left(\frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2}ight) 	imes 2+\left(\frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2}ight) 	imes 3$

$=\frac{1}{4}+\frac{1}{4}+\frac{3}{16}=\frac{11}{16}$

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