Question

Suppose 60% of jurors come to a just decision. In a jury of 10 people, what is the probability that more than half come to a just decision?

a. 0.367
b. 0.201
c. 0.633
d. 0.251

Answer 1

To find the probability that more than half of the jurors come to a just decision, we can use the binomial probability formula. The probability that a juror comes to a just decision is 60%, so the probability that a juror does not come to a just decision is 40%. Using the binomial probability formula, we can calculate the probabilities of having 6, 7, 8, 9, or 10 jurors come to a just decision and sum them up to find the probability that more than half come to a just decision, which is 0.633.

Step-by-step explanation:

To find the probability that more than half of the jurors come to a just decision, we can use the binomial probability formula. The probability of a juror coming to a just decision is 60%, so the probability of a juror not coming to a just decision is 40%. Since we want more than half of the jurors to come to a just decision, we are interested in the probabilities of having 6, 7, 8, 9, or 10 jurors come to a just decision.

Using the binomial probability formula, we can calculate these probabilities:

1. P(6 jurors come to a just decision) = C(10, 6) * 0.6^6 * 0.4^4 = 0.2508
2. P(7 jurors come to a just decision) = C(10, 7) * 0.6^7 * 0.4^3 = 0.2149
3. P(8 jurors come to a just decision) = C(10, 8) * 0.6^8 * 0.4^2 = 0.1209
4. P(9 jurors come to a just decision) = C(10, 9) * 0.6^9 * 0.4^1 = 0.0403
5. P(10 jurors come to a just decision) = C(10, 10) * 0.6^10 * 0.4^0 = 0.006

Adding up these probabilities gives us:

P(more than half come to a just decision) = 0.2508 + 0.2149 + 0.1209 + 0.0403 + 0.006 = 0.633

Therefore, the probability that more than half of the jurors come to a just decision is 0.633.