Answer:
Option E
[tex]\frac{16}{21}[/tex]
Step-by-step explanation:
Number of ways of selecting two people from a group of seven people is
[tex]C^2_{7}[/tex]
[tex]\frac{7 * 6* 5!}{2*1* 5!} \\= 21[/tex]
Number of ways by which two people selected in a room come out to be siblings are -
[tex]C^2_{2}[/tex]+[tex]C^2_{3}[/tex]+ [tex]C^2_{2}[/tex]
[tex]= \frac{2*1}{2*1} + \frac{3*2*1}{2*1} + \frac{2*1}{2*1}\\= 1+ 3+1\\= 5[/tex]
Number of ways by which two people selected in a room are not siblings
[tex]= 1-[/tex]Probability of selecting two siblings
[tex]= 1-\frac{5}{21} \\= \frac{16}{21}[/tex]
Hence, option E is correct
