Respuesta :
Answer: The answer is 77% (approximately).
Step-by-step explanation: Given that a bag contains 11 diamonds, out of which 6 are real and 5 are fake. 6 diamonds are picked from the bag randomly. We are to calculate the probability that at most four of the 6 diamonds are real.
Since we can choose at most 4 real diamonds, so the number of ways in which we can do so is given by
[tex]n=\dfrac{5!}{5!0!}\times \dfrac{6!}{1!5!}+\dfrac{5!}{4!1!}\times \dfrac{6!}{2!4!}+\dfrac{5!}{3!2!}\times \dfrac{6!}{3!3!}+\dfrac{5!}{4!1!}\times \dfrac{6!}{4!2!}\\\\\\\Rightarrow n=1\times6+5\times 15+10\times20+5\times 15\\\\\Rightarrow n=6+75+200+75\\\\\Rightarrow n=356.[/tex]
And the total number of ways in which we can choose 6 diamonds out of 11 is
[tex]N=\dfrac{11!}{6!5!}=462.[/tex]
Therefore, the required probability will be
[tex]p=\dfrac{n}{N}=\dfrac{356}{462}\sim .77=77\%.[/tex]
Thus, the probability is 77% approx.
