Assume that when adults with smartphones are randomly selected, 56% use them in meetings or classes. If 11 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.

Step-by-step explanation:

Use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Here, n = 11, p = 0.56, q = 0.44, and r = 0, 1, or 2.

P = ₁₁C₀ (0.56)⁰ (0.44)¹¹ + ₁₁C₁ (0.56)¹ (0.44)¹⁰ + ₁₁C₂ (0.56)² (0.44)⁹

P = (0.44)¹¹ + 11 (0.56) (0.44)¹⁰ + 55 (0.56)² (0.44)⁹

P ≈ 0.0125