Pharmaceutical companies advertise for the birth control pill an annual efficacy of 98.6% in preventing pregnancy. However, under typical use the real efficacy is only about 95%. That is, 5% of women taking the pill for a year will experience an unplanned pregnancy that year. The difference between these two rates is that the real world is not perfect: for example, a woman might get sick or forget to take the pill one day, or she might be prescribed antibiotics which interfere with hormonal metabolism. If a sexually active woman takes the pill for the four years she is in college, what is the chance that she will become pregnant at least once? (Assume that the chance of pregnancy for each year is independent).
To calculate the probability of getting pregnant at least once in the four years, we first calculate the probability of NOT getting pregnant each year and then multiply those probabilities together to find the probability of not getting pregnant throughout all four years. Finally, we subtract that probability from 1 to find the probability of getting pregnant at least once.
The probability of not getting pregnant in a single year is 1 - 0.05 = 0.95.
The probability of not getting pregnant all four years = 0.95 * 0.95 * 0.95 * 0.95 = 0.8145 (rounded to four decimal places).
Finally, the probability of getting pregnant at least once in the four years = 1 - 0.8145 = 0.1855, or about 18.55%.
To calculate the chance that a sexually active woman taking the birth control pill for four years of college will become pregnant at least once, we can use the concept of complementary probabilities.
First, let's calculate the probability of not becoming pregnant in a given year, assuming a 95% efficacy rate under typical use. Since the efficacy rate is the complement of the pregnancy rate, the probability of not becoming pregnant in a given year is 1 - 0.05 = 0.95.
Since each year is independent, the probability of not becoming pregnant in all four years is calculated by multiplying the probabilities of not becoming pregnant in each individual year:
0.95 * 0.95 * 0.95 * 0.95 = 0.8145
This means that the chance of not becoming pregnant in all four years is 0.8145.
To find the chance of becoming pregnant at least once, we can subtract the probability of not becoming pregnant in all four years from 1:
1 - 0.8145 = 0.1855
Therefore, the chance that a sexually active woman taking the pill for four years of college will become pregnant at least once is approximately 18.55%.
To find the chance that a sexually active woman taking the birth control pill for four years of college will become pregnant at least once, we can use the concept of complementary probability.
First, let's calculate the probability of not becoming pregnant in a single year using the real efficacy rate of 95%. The probability of not becoming pregnant in a single year is 1 minus the probability of becoming pregnant, which is 1 - 0.95 = 0.05.
Since the chance of pregnancy for each year is independent, the probability of not becoming pregnant in four consecutive years is (0.05)^4 = 0.00000625.
To find the chance of becoming pregnant at least once in four years, we can subtract the probability of not becoming pregnant from 1:
1 - 0.00000625 = 0.99999375
Therefore, the chance that a sexually active woman taking the birth control pill for the four years of college will become pregnant at least once is approximately 0.99999375, or about 99.999375%.
It is important to note that this calculation assumes the efficacy rates remain constant throughout the four years and other factors influencing pregnancy are not considered, such as using additional contraceptive methods or encountering reproductive health issues.