A group of teenager smoking rate dropped 8.5% in 2007 from 17.6% in 2001 and 23% in 1997. 1. Calculate the probability that at least one in a group of 10 teenagers smoked in 2007.2. Calculate the probability that at least one in a group of 10 teenagers smoked in 2001. 1. Calculate the probability that at least one in a group of 10 teenagers smoked in 1997.
1) .206523
2) .54748
3) .707884
Correction:
3) .206523
2) .54748
1) .707884
To calculate the probability, we need to determine the rate at which each teenager smokes, and then use that rate to calculate the probability of at least one teenager smoking in each given year.
1. To calculate the probability that at least one in a group of 10 teenagers smoked in 2007:
- The smoking rate in 2007 is 8.5%.
- We can calculate the probability that a teen does not smoke as (100% - 8.5%) = 91.5%.
- The probability that none of the ten teenagers smoke is (91.5%)^10.
- Therefore, the probability that at least one teenager smokes is 1 - (91.5%)^10.
2. To calculate the probability that at least one in a group of 10 teenagers smoked in 2001:
- The smoking rate in 2001 is 17.6%.
- We can calculate the probability that a teen does not smoke as (100% - 17.6%) = 82.4%.
- The probability that none of the ten teenagers smoke is (82.4%)^10.
- Therefore, the probability that at least one teenager smokes is 1 - (82.4%)^10.
3. To calculate the probability that at least one in a group of 10 teenagers smoked in 1997:
- The smoking rate in 1997 is 23%.
- We can calculate the probability that a teen does not smoke as (100% - 23%) = 77%.
- The probability that none of the ten teenagers smoke is (77%)^10.
- Therefore, the probability that at least one teenager smokes is 1 - (77%)^10.
.5887
.8557
.9276