A recent survey found that 70% of all adults over 50 wear sunglasses for driving. in a random sample of 10 adults over 50, what is the probability that at least six wear sunglasses? round to the nearest thousandth.

The solution for this problem is to use the binomial distribution because you can either wear glasses or you don't wear glasses. Attempts are autonomous since glasses of one doesn't affect the other.

P[x>=6] = P[x=6] + P[x=7] + P[x=8] + P[x=9] + P[x=10] (10 choose 6) * (.70) ^ 6 * (.30) ^ 4 + (10 choose 7) * (.70) ^ 7 * (.30) ^ 3 + (10 choose 8) * (.70) ^ 8 * (.30) ^ 2 + (10 choose 9) * (.70) ^ 9 * (.30) ^ 1 + (10 choose 10) * (.70) ^ 10 * (.30) ^ 0 =.8497 or. 850

note: n choose k is the combination formula