Question

three types of bulbs A,B,C are purchased in an electric company ,due to thier lives bulb A is twice as likely to be purchased as B, and blub B is twice as likely to be purchased as C. A bulb is chosen at random what is probability blub is A or B.

Answer 1

Answer on Question #81477 – Math – Statistics and Probability

Question

Three types of bulbs $A, B, C$ are purchased in an electric company, due to their lives bulb $A$ is twice as likely to be purchased as $B$, and bulb $B$ is twice as likely to be purchased as $C$. A bulb is chosen at random what is probability bulb is $A$ or $B$.

Solution

$$\begin{array}{l} P(A) = 2P(B), P(B) = 2P(C) \\ P(A) + P(B) + P(C) = 1 \\ 2(2P(C)) + 2P(C) + P(C) = 1 \\ P(C) = \frac{1}{7} \\ \end{array}$$ $$P(A \cup B) = P(\overline{C}) = 1 - P(C) = 1 - \frac{1}{7} = \frac{6}{7}$$

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