A jury panel consists of 3 juries that are randomly voting in a topic. Each jury

Question

A jury panel consists of 3 juries that are randomly voting in a topic. Each jury can decide to either be in favor (F), opposed (O) or to abstain (T). An outcome for the panel decision then consists of the 3 random votes. (a) What is n(S), the number of outcomes of the sample space? (b) Let the event A be that all three juries vote in the same way. Find the probability P(A) (c) Let the event B be that all three juries vote different from each other. Find P(B). (d) Find the probabilities P(A), PA u B), and P(AnB).

Explanation / Answer

Answer to each question is as follows. Write back to me in case of doubts:

a. Each of jury members can vote F, O or T. So, 3 *3 *3 = 27 combinations possible

n(S) = 27

b. P(A) = ?

When all 3 will be either of the F or O or T

So, P(A) = 3/27 = 1/9

c. So. when 1st member votes F, 2nd can vote for O or T. Then 3rd member has only 1 option

So, 1st member choosen option in 3 ways (F or O or T)
2nd member has 2 options, 3rd has choose the last remaining option
So, n(B) = 3*2*1 = 6 ways

P(B) = 6/27 = 2/9

d.

P(A') = 1-P(A) = 8/9

P(A U B) = P(A)+P(B) - P( A & B) = (1/9)+(2/9)- P(A & B)

P(A & B) = 0, as the events of 'voting same' and 'voting different' are mutually exclusive

Hence, P(A U B) = 3/9 = 1/3

P( A & B) = 0

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