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 being selected is equally likely. Find the probability that at least 20 characters in the ID are numbers. Use Excel to find the probability.

0.578

Step-by-step explanation:

There are 10 numbers from 0 to 9.

There are 6 letters from A to F.

Each letter and number is equally likely, so the probability that a character is a number is 10/16 = 5/8.

The probability that there are exactly r letters can be found with binomial probability.

P = nCr pʳ qⁿ⁻ʳ

Given that n = 32, p = 5/8, and q = 3/8, you can use Excel to find each probability from r=20 to r=32, then add them all up.

P = ₃₂C₂₀ (⅝)²⁰ (⅜)³²⁻²⁰ + ₃₂C₂₁ (⅝)²¹ (⅜)³²⁻²¹ + ... + ₃₂C₃₂ (⅝)³² (⅜)³²⁻³²

P = 0.578

Alternatively, you can use the BINOM.DIST function in Excel to find the cumulative probability.

P(at least 20) = 1 − P(at most 19)

P = 1 − BINOM.DIST(19, 32, 0.625, TRUE)

P = 0.578

df =

both have same length