Answer:0.0128
Step-by-step explanation:
Given
There are 35 gems out of which there are 10 real diamonds and 25 are fake diamonds.
Probability that the last gem burglar steals is second real diamond in the set of four
there can three possibilities
a)Real , fake, fake , real
b)fake , real , fake , real
c)fake, fake, real ,real
a)[tex]P=\frac{10}{35}\times \frac{25}{34}\times \frac{24}{33}\times \frac{9}{32}=\frac{25\times 24\times 10\times 9}{35\times 34\times 33\times 32}[/tex]
b)[tex]P=\frac{25}{35}\times \frac{10}{34}\times \frac{24}{33}\times \frac{9}{32}=\frac{25\times 24\times 10\times 9}{35\times 34\times 33\times 32}[/tex]
c)[tex]P=\frac{25}{35}\times \frac{24}{34}\times \frac{10}{33}\times \frac{9}{32}=\frac{25\times 24\times 10\times 9}{35\times 34\times 33\times 32}[/tex]
[tex]P_{total}=3\times =\frac{25\times 24\times 10\times 9}{35\times 34\times 33\times 32}=\frac{54000}{1256640}=0.0128[/tex]
