Answer:
0.933 ( approx )
Step-by-step explanation:
Given,
Real diamonds = 6,
Fake diamonds = 5,
Total diamonds = 6 + 5 = 11,
If six diamonds are picked from the bag at random,
So, the total ways = [tex]^{11}C_6[/tex]
[tex]=\frac{11!}{6!5!}[/tex]
= 462
Also, the number of ways of at most four real diamonds in these 6 diamonds
[tex]=^{6}C_1\times ^{5}C_5 + ^{6}C_2\times ^{5}C_4+^{6}C_3\times ^{5}C_3+^{6}C_4\times ^{5}C_2[/tex]
[tex]=6+75+200+150[/tex]
[tex]=431[/tex]
Hence, the probability that at most four of them are real = [tex]\frac{431}{462}[/tex]
[tex]\approx 0.933[/tex]
