Final answer:
To find the probability that no more than one adult needs correction eyeglasses out of a group of 15 adults, we can use the binomial probability formula. By calculating the probabilities for zero and one adult needing correction eyeglasses, we can find the answer.
Step-by-step explanation:
The question is asking for the probability that no more than one adult out of fifteen needs correction eyeglasses for their eyesight, given that 71% of adults need correction eyeglasses.
To find this probability, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of getting exactly k successes
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success (in this case, the probability that an adult needs correction eyeglasses)
- n is the number of trials (in this case, the number of adults)
- k is the number of successes (in this case, the number of adults who need correction eyeglasses)
In this case, we want to find the probability that no more than one adult needs correction eyeglasse. So we need to calculate:
P(X = 0) + P(X = 1)
Plugging in the values:
P(X = 0) = C(15, 0) * 0.71^0 * (1 - 0.71)^(15 - 0)
P(X = 1) = C(15, 1) * 0.71^1 * (1 - 0.71)^(15 - 1)
Calculating these probabilities will give us the answer.