A database system assigns a 32-character ID to each record, where each character is either a number from 0 to 9 or a letter from A to F. Assume that each number or letter is equally likely. Find the probability that at least 16 characters in the ID are numbers. Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.

0.948

Step-by-step explanation:

Given that:

Number of character ID = 32

Numbers = 0 - 9 = 10

Alphabets = A - F = 6

Likelihood of each number or alphabet is equal

Probability that atleast 16 characters in the ID are numbers

Probability of success (p) = required outcome / Total possible outcomes

p = 10/(10 + 6) = 5/8

P(at least 16 numbers), similar to 1 - p(at most 15)

Using the specified calculator :

Binomcdf(number of trials, p, 15) = 0.0520

1 - 0.0520 = 0.948

Divide 10680 by 200 to get 53.4 months.

If you set the average month as 30 days, the answer is:

53 months and 12 days or

4 years 5 months and 12 days