Bunuel wrote:
After each throw of a red die, the top face is marked with a blue stripe. What is the probability that after 6 throws all faces of the die will be marked blue?
A. 3/126
B. 5/324
C. 1/54
D. 2/91
E. 5/216
After every throw, the top face of the red die is marked with a blue stripe. We are
asked to find the probability that all the 6 faces of the die are marked blue in the
first 6 throw(s)
This is possible when each and every throw yields a different number. The first throw
could yield any of the 6 digits. The second throw can be anything but the digit we get
in the first throw. Similarly, the third number could be any other digit except the digit
which we get in the first and second throws.
The probability is \(1*\frac{5}{6}*\frac{4*3}{6*6}*\frac{2}{6}*\frac{1}{6} = \frac{5}{6}*\frac{1}{3}*\frac{1}{3}*\frac{1}{6} = \frac{5}{324}\)
(Option B)
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