14.Probability
easy

दो पुरुषों व दो स्त्रियों के समूह में से दो व्यक्तियों की एक समिति का गठन करना है। प्रायिकता क्या है कि गठित समिति में एक पुरुष हो ?

A

$\frac{2}{3}$

B

$\frac{2}{3}$

C

$\frac{2}{3}$

D

$\frac{2}{3}$

Solution

The total number of persons $=2+2=4 .$ Out of these four person, two can be selected in $^{4} C _{2}$ ways.

One man in the committee means that there is one woman. One man out of $2$ can be selected in $^{2} C _{1}$ ways and one woman out of $2$ can be selected in $^{2} C _{1}$ ways.

Together they can be selected in $^{2} C _{1} \times^{2} C _{1}$ ways.

Therefore $P$ (One man) $=\frac{^{2} C _{1} \times^{2} C _{1}}{^{4} C _{2}}$ $=\frac{2 \times 2}{2 \times 3}=\frac{2}{3}$

Standard 11
Mathematics

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