Question

A certain 5-digit combination lock can be reset with a new combination. The lock uses numbers from 1 to 6. After a friend accidentally resets it to an unknown combination, what is the probability that you guess the combination that opens the lock?
A.
100,000

B.
7,776

C.
1100,000
D.
17,776

Answer 1

Answer:

B.7,776

Step-by-step explanation:

You can try to guess the combination but the probability that you do it with no clues its 1 in 7,776 times, because you have six numbers in each position and have 6 positions, to guess one number would be 1/6, now you multiply that by the second, then the third, then the fourth, then the fifth. and you get your probability:

$Probability:(Probability1)*(Probability2)*(Probability3)*(Probability4)*(Probability5)$

$Probability=(\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )(\frac{1}{6} )$

$Probability=\frac{1}{6^{5} } =\frac{1}{7776}$

That´s why the probability is 1 in 7,776

Answer 2

Answer:

1 / 7776

Step-by-step explanation:

The probability of guessing 1 number in any of the 5 positions is 1/6 .

So the probability of doing this 5 times = (1/6)^5   = 1 / 7776.