Answer:
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
