Respuesta :
Answer:
(a) The different possible dial combinations for the lock on the bank vaults is 27,000.
(b) The probability that a randomly select a position on each dial will open the bank vault is [tex]\frac{1}{27000}[/tex].
Step-by-step explanation:
A bank vault has 3 dials each with 30 positions.
(a)
For the vault to open each dial must be at a certain position.
For dial 1 there are 30 ways to position the dial.
For dial 2 also there are 30 ways to position the dial.
Similarly for dial 3 there are 30 ways to position the dial.
The total number of combinations of the three dials is: [tex]=30\times30\times30=27000[/tex]
Thus, the different possible dial combinations for the lock on the bank vaults is 27,000.
(b)
The probability that a randomly select a position on each dial will open the bank vault is:
[tex]P(Correct\ positions)=\frac{1}{27000}[/tex]
Thus, the probability that a randomly select a position on each dial will open the bank vault is [tex]\frac{1}{27000}[/tex].
(c)
It is provided that each of the three dials must be in the correct position for the lock to open.
This implies that only 1 combination of the three dials opens the vault.
Thus, the probability of selecting the correct position of the three dials is [tex]\frac{1}{27000}[/tex].
