Answer:
0.033
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ (1−p)ⁿ⁻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, p = 0.5, q = 0.5, and n = 11.
We need to find P when r is 0, 1, and 2, then add up the results to get the total probability.
r = 0:
P = ₁₁C₀ (0.5)⁰ (0.5)¹¹⁻⁰
P ≈ 0.0005
r = 1:
P = ₁₁C₁ (0.5)¹ (0.5)¹¹⁻¹
P ≈ 0.0054
r = 2:
P = ₁₁C₂ (0.5)² (0.5)¹¹⁻²
P ≈ 0.0269
Therefore, the total probability is:
P = 0.0005 + 0.0054 + 0.0269
P = 0.0328
Round to the thousandths place, the probability is 0.033.
