Step 1 :This is a binomial probability problem. We are given that the probability of success (an adult needing eyesight correction) is 0.78. We are asked to find the probability of 0 or 1 success in 15 trials. We can use the binomial probability formula to solve this problem.
Step 2 :The binomial probability formula is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\) where: \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) is the number of combinations of n items taken k at a time, p is the probability of success, and n is the number of trials.
Step 3 :We need to calculate \(P(X=0)\) and \(P(X=1)\), and then add these two probabilities together to get the final answer.
Step 4 :Given p = 0.78 and n = 15, we calculate \(P_0 = 1.368800680154118e-10\) and \(P_1 = 7.279530889910539e-09\).
Step 5 :The final probability is the sum of \(P_0\) and \(P_1\), which is \(7.416410957925951e-09\).
Step 6 :The final probability is extremely small, much less than 0.05. This means that the probability of no more than 1 out of 15 adults needing eyesight correction is very low.
Step 7 :Final Answer: The probability that no more than 1 out of 15 adults need eyesight correction is approximately \(\boxed{7.416 \times 10^{-9}}\). Therefore, the answer to the question 'Is 1 a significantly low number of adults requiring eyesight correction?' is 'Yes, because the probability of this occurring is small.'