Consider a box containing four balls: one red, one green, one blue, and one tric

Question

Consider a box containing four balls: one red, one green, one blue, and one tricolor (=red,green and blue). You draw one ball from the box. Consider the three events:

R = {the drawn ball contains red}
G = {the drawn ball contains green}
Y = {the drawn ball contains red and green}

1. Are R and G independent?

2. Are G and Y independent?

3. Are R and Y independent?

4. Let A, B, C be three events. Is the following statement true? Justify your answer. “If A and B are independent, and B and C are independent, then A and C are independent.”

Explanation / Answer

P(R) = P(G) = P(B) = 2/4 = 1/2

P(G|R) = P(R|G) = P(B|G) = P(G|B) = P(R|B) = P(B|R) = 1/2

1. Since P(G|R) = P(R|G) = P(R) = P(G), R and G are independent.

2. Since P(G|Y) = P(Y|G) = P(Y) = P(G), Y and G are independent.

3. Since P(Y|R) = P(R|Y) = P(R) = P(Y), R and Y are independent.

4. The statement is false.

Consider A = C.

A and B are independent and B and C are independent.

But A and C are not independent since P(A|C) = P(C|A) = 1.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.