Question

A lock on a bank vault consists of three dials, each with 30 positions. In order for the vault to open, each of the three dials must be in the correct position. a. How many different possible dial combinations are there for this lock? b. What is the probability that if you randomly select a posi- tion on each dial, you will be able to open the bank vault? c. Explain why

Answer 1

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 $\frac{1}{27000}$.

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: $=30\times30\times30=27000$

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:

$P(Correct\ positions)=\frac{1}{27000}$

Thus, the probability that a randomly select a position on each dial will open the bank vault is $\frac{1}{27000}$.

(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 $\frac{1}{27000}$.