A chain of video stores sells three different brands of DVD players (labeled bra

Question

A chain of video stores sells three different brands of DVD players (labeled brands 1,2, and 3). 50% are brand 1, 30% are brand 2, and 20% are brand 3. 2 3 It is known that 25% of brand 1 DVD players will require warranty repair work, and corresponding percentages for brands 2 and 3 are 20% and 10%, respectively Find the probability that a randomly chosen DVD.. 1) is brand 1 and requires repair work 2) needs repair. HINT: Define events such as B1 (from brand 1) or R (needs repair). Use probability rules to solve.

Explanation / Answer

P(B1) = 0.5, P(B2) = 0.3 and P(B3) = 0.2

P(B1 | R1) = 0.25, P(B2 | R2) = 0.2 and P(B3 | R3) = 0.1

(1) Required probability P(B1 and R1) = P(B1) * P(B1 | R1) = 0.5 * 0.25 = 0.125

(2) Required Probability = P(B1 and R1) + P(B2 and R2) + P(B3 and R3)

= 0.5*0.25 + 0.3*0.2 + 0.2*0.1 = 0.205

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