What is the probability that a seven-digit phone number contains the number 7?

What is the probability that a seven-digit phone number contains the number 7?

asked 2021-01-15
What is the probability that a seven-digit phone number contains the number 7?

Answers (1)

Assuming that the number 7 must appear at least once, we find its complement first, which is not a phone number with number 7. The probability of not having a 7 is 9/10 (there are 10 possible digits). Hence,
Hence, the probability that there is at least 1 number 7 is:
P(at least one 7)=1-P(no 7)
P(at least one 7)=\(\displaystyle{1}-{\left(\frac{{9}}{{10}}\right)}^{{7}}\)
P(at least one 7)\(\displaystyle\sim{0.522}\to{52.2}\%\)

Relevant Questions

asked 2020-12-17
A bag contains 7 tiles, each with a different number from 1 to 7. You choose a tile without looking, put it aside, choose a second tile without looking, put it aside, then choose a third tile without looking. What is the probability that you choose tiles with the numbers 1, 2, and 3 in that order?
asked 2021-02-26
Census reports for a city indicate that 62% of residents classify themselves as Christian, 12% as Jewish , and 16% as members of other religions (Muslims, Buddhists, etc.).
The remaining residents classify themselves as nonreligious.
A polling organization seeking information about public opinions wants to be sure to talk with people holding a variety of religious views, and makes random phone calls. Among the first four people they call, what is the probability they reach a) all Christians? b) no Jews? c) at least one person who is nonreligious?
asked 2020-10-19
A manufacturer of digital phones has the following probability distribution for the number of defects per phone: xf(x) .89 1.07 2.03 3.01
(a) Determine the probability of 2 or more defects. (b) Is a randomly selected phone more likely to have 0 defects or 1 or more defects?
asked 2021-02-21
Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0.
asked 2021-02-04
A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find each probability. drawing a yellow chip, replacing it, and choosing a blue chip.
asked 2020-11-26
A bag contains 6 red, 4 blue and 8 green marbles. How many marbles of each color should be added so that the total number of marbles is 27, but the probability of randomly selecting one marble of each color remains unchanged.
asked 2021-01-24
If you used a random number generator for the numbers from 1 through 20 to play a game, what is the theoretical probability of getting each of these outcomes? a. A multiple of 3 or a multiple of 7, P(multiple of 3 or multiple of 7) b. P( even or odd) c. P(prime or 1) d. How did you find the probabilities of these events?
asked 2021-01-27
Charlie and Clare are playing a number-guessing game. Charlie picked two numbers between 1 and 5. To win the game, Clare must guess both his numbers in three lines. Her guesses, simulated using a random-number generator are shown in the table. If Charlie's numbers are 1 and 3, what is the experimental probability that Clare won?
asked 2021-04-13
To find:
The smallest the smallest positive integer such that if we divide it by two, three and four, the remainder is one but seven divides the number evenly.
asked 2021-02-19
The diagram shows a spinner. When the arrow is spun the probability of scoring a 2 is 0.3 . The arrow is spun twice and the scores are added. What is the probability that the total score is 6?6? Express the answer as a decimal. [ \sqrt { 2 } \text { . } ]