what is the probability that a 6 digit phone number contains at least one 8?
must be an old-type "crank on the wall" from The Waltons era ....
anyway ....
I will assume that none of your 6 digit numbers can start with a zero, and that numbers may be repeated,
so we can't have a number with no 8
prob of no 8
= 8 x 9^5/(9x10^5)
so prob that it contains at least one 8
= 1 - (8x9^5)/(9x10^5)
= appr 0.475
The U.S. has no six-digit phone numbers.
To find the probability that a 6-digit phone number contains at least one 8, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Calculate the number of favorable outcomes:
To have at least one 8 in a 6-digit phone number, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
In this case, the event not occurring means that none of the digits from 0 to 9 in the phone number is an 8. Since there are 10 possible digits (0-9), the probability of not having an 8 in a single digit is 9/10.
To find the probability of not having an 8 in any of the 6 digits, we multiply this probability by itself 6 times since each digit is independent:
(9/10) * (9/10) * (9/10) * (9/10) * (9/10) * (9/10) = (9/10)^6
Since we want the number of favorable outcomes (i.e., having at least one 8), we subtract the probability of not having an 8 from 1:
1 - (9/10)^6 = 1 - 0.531441 ≈ 0.468559
Step 2: Calculate the total number of possible outcomes:
For a 6-digit phone number, each digit can be any number from 0 to 9. So, there are 10 choices for each digit.
To find the total number of possible outcomes, we multiply 10 by itself 6 times:
10^6 = 1,000,000
Step 3: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes = 0.468559 / 1,000,000 ≈ 0.0004686
Therefore, the probability that a 6-digit phone number contains at least one 8 is approximately 0.0004686 or about 0.0469%.