Q and R are independent events. P ( Q ) = 0.4; P ( Q AND R ) = 0.08. Find P ( R

Question

Q and R are independent events. P(Q) = 0.4; P(Q AND R) = 0.08. Find P(R).
P(R) =

Suppose that you have 10 cards. 4 are green and 6 are yellow. The 4 green cards are numbered 1, 2, 3, and 4. The 6 yellow cards are numbered 1, 2, 3, 4, 5, and 6. The cards are well shuffled. You randomly draw one card.

• G = card drawn is green
• Y = card drawn is yellow
• E = card drawn is even-numbered

Part (a)

List the sample space. (Type your answer using letter/number combinations separated by commas. Example: G1, Y1, ...)

Explanation / Answer

(1)

Given:
P(Q) = 0.4

P(Q AND R) = 0.04

Since Q and R are independent, by multiplication theorem:
P(Q AND R) = P(Q) P(R)

Substituting, we get:

0.04 = 0.4 P(R)

So,

P(R) = 0.04/0.4 = 0.1

(2) Sample space = {G1, G2, G3, G4, Y1,Y2,Y3,Y4,Y5,Y6}

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