Answer:
The probability that all 14 bits are 1s = 0.000061
Step-by-step explanation:
Probability that a bit is 1 is p = 0.5
Probability that a bit isn't 1 is q = 1 - 0.5 = 0.5
This is a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 14
x = Number of successes required = 14
p = probability of success = 0.5
q = probability of failure = 0.5
P(X = 14) = ¹⁴C₁₄ (0.5)¹⁴ (0.5)¹⁴⁻¹⁴
P(X = 14) = ¹⁴C₁₄ (0.5)¹⁴ (0.5)⁰
P(X = 14) = 1 (0.000061)(1) = 0.000061
