A combination lock has 10 dials. To
open the lock, you must turn the dial right to the first number, left to
the second number. What is the probability that you choose the correct combination?
To find the probability of choosing the correct combination on a combination lock with 10 dials, we need to determine the number of possible combinations and the number of favorable outcomes.
Each dial can be set to any of the 10 numbers, so there are 10 choices for each dial. Since there are 10 dials, we can calculate the total number of combinations by multiplying the choices for each dial: 10 * 10 * 10 * ... * 10 (10 times in total).
Using exponentiation notation, this is written as 10^10, which equals 10 billion possible combinations.
Now, the favorable outcome is the correct combination. Since we are given that the lock must be turned right to the first number and left to the second number, there is only one specific combination that will work.
Therefore, the number of favorable outcomes is 1.
To calculate the probability, we divide the number of favorable outcomes by the number of possible outcomes:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 1 / 10^10
Simplifying this, the probability is 1 in 10 billion, which is an incredibly low probability.
In conclusion, the probability of choosing the correct combination on this lock is extremely low, with odds of 1 in 10 billion.