Question

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

Answer 1

D. 0.6331

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