Suppose 60% of jurors come to a just decision. In a jury of ten people, what is the probability more than half come to a just decision?

A. 0.3669

B. 0.3823

C. 0.6177

D. 0.6331

E. 0.8494

D. 0.6331

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 1-p, the probability of failure.

More than half of 10 jurors is 6, 7, 8, 9, and 10. Find the probability of each.

If r = 6:

P = ₁₀C₆ (0.6) ⁶ (0.4) ⁴

P = 0.2508

If r = 7:

P = ₁₀C₇ (0.6) ⁷ (0.4) ³

P = 0.2150

If r = 8:

P = ₁₀C₈ (0.6) ⁸ (0.4) ²

P = 0.1209

If r = 9:

P = ₁₀C₉ (0.6) ⁹ (0.4) ¹

P = 0.0403

If r = 10:

P = ₁₀C₁₀ (0.6) ¹⁰ (0.4) ⁰

P = 0.0060

Therefore, the total probability is:

P = 0.2508 + 0.2150 + 0.1209 + 0.0403 + 0.0060

P = 0.6330