The probability of hitting a target by three | vedclass

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Question

$\lambda  = \overline {m{A}} {m{BC}} + \overline {m{B}} {m{CA}} + \overline {m{C}} {m{AB}}$

$=\left(\frac{1}{2} 	imes \frac{1}{3}

Vedclass · Accepted Answer

$\frac{13}{24}$

Vedclass · Answer

$\lambda  = \overline {m{A}} {m{BC}} + \overline {m{B}} {m{CA}} + \overline {m{C}} {m{AB}}$

$=\left(\frac{1}{2} 	imes \frac{1}{3} 	imes \frac{1}{4}ight)+\left(\frac{2}{3} 	imes \frac{1}{4} 	imes \frac{1}{2}ight)+\left(\frac{3}{4} 	imes \frac{1}{2} 	imes \frac{1}{2}ight)=\frac{6}{24}=\frac{1}{4}$

$\mu=\lambda+\mathrm{ABC}=\frac{1}{4}+\left(\frac{1}{2} 	imes \frac{1}{3} 	imes \frac{1}{4}ight)=\frac{7}{24}$

$\lambda+\mu=\frac{1}{4}+\frac{7}{24}=\frac{13}{24}$

The probability of hitting a target by three marks men is $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability that exactly two of them will hit the target is $\lambda$ and that at least two of them hit the target is $\mu$ then $\lambda + \mu$ is equal to :-

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