This post covers Introduction to probability from Statistics for Engineers and Scientists by William Navidi.

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• An electrical engineer has on hand two boxes of resistors, with four resistors in eachbox. The resistors in the first box are labeled $10 Ω (ohms)$, but in fact their resistances are $9$, $10$, $11$, and $12 Ω$. The resistors in the second box are labeled $20 Ω$, but in fact their resistances are $18$, $19$, $20$, and $21 Ω$. The engineer chooses one resistor from each box and determines the resistance of each. Let $A$ be the event that the first resistor has a resistance greater than $10$, let $B$ be the event that the second resistor has a resistance less than $19$, and let $C$ be the event that the sum of the resistances is equal to $28$. Find a sample space for this experiment, and specify the subsets corresponding to the events $A$, $B$, and $C$.

  • A good sample space for this experiment is the set of ordered pairs in which the first component is the resistance of the first resistor and the second component is the resistance of the second resistor.

    S = {(9, 18), (9, 19), (9, 20), (9, 21), (10, 18), (10, 19), (10, 20),(10, 21), (11, 18), (11, 19), (11, 20), (11, 21), (12, 18), (12, 19), (12, 20), (12, 21)}​

    The events $A$, $B$, and $C$ are given by

    $A = {(11, 18), (11, 19), (11, 20), (11, 21), (12, 18), (12, 19), (12, 20), (12, 21)}$

    $B = {(9, 18), (10, 18), (11, 18), (12, 18)}$

    $C = {(9, 19), (10, 18)}$