Question

a database system assigns a 32 character ID to each record, where each character is either a number from 0-9 or a letter from A-F. Assume that each number or letter being selected is equally likely. Find the probability that At Least 20 characters in the ID are numbers. Use excel to find the probability. Round to three decimal places.

Answer 1

total number of digits= 10 (from 0 to 9)

total number of letters = 6 (from A to F)

probability of numbers = 10/(10+6) = 0.625

this is a case of binomial distribution with fixed number trials n = 32 and probability p = 0.625

we have to find probability of at least 20 numbers

P(at least 20 numbers) = 1 - BINOMDIST(numbers, trials, probability,true)

setting numbers = 20-1, trials = 32 and probability = 0.625

we get

(BINOMDIST is excel function)

P(X > 20) = 1 - BINOMDIST(20 - 1,32,0.625, true = 1-0.4219 = 0.578