After each throw of a red die, the face that shows is marked with a

Question

After each throw of a red die, the face that shows 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. 4/216

D. 4/182

E. 5/216

Sasindran · Answer

B

Chances of marking a blue face on first throw=6/6. Whatever be the face we can mark it blue. 
Similarly in second throw=5/6
Third throw=4/6
Fourth throw=3/6
Fifth throw=2/6
Sixth throw=1/6

Hence the total probability is 6/6*5/6*4/6*3/6*2/6*1/6= 5/324

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pushpitkc · Answer

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)

GMATinsight · Answer

Total Outcomes = 6^6 . (Cause any one of the six faces may appear on the top in each throw)

Favourable outcomes = 6*5*4*3*2*1 = 6! = 720 (Cause the top face shouldn't repeat hence there are 6 acceptable outcomes for the first throw and subsequently 5 acceptable as the face earlier obtained shouldn't repeat and so on...

Probability = 720/6^6 = 5/324

Answer: Option B

JeffTargetTestPrep · Answer

There is a 1/1 chance of rolling any number on the first roll, after which the side with that number is marked with blue. In the second roll, there is a 5/6 probability that a red side shows up; in the third roll, there is a 4/6 probability that a red side shows up, and so on. .

The total probability is:

1 x 5/6 x 4/6 x 3/6 x 2/6 x 1/6

1 x 5/6 x 2/3 x 1/2 x 1/3 x 1/6 = 10/648 = 5/324

Answer: B

After each throw of a red die, the face that shows is marked with a

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