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A sample of ore is found to be 0.0095 % silver and 0.036 % copper. What is the percentage of...

Question:

A sample of ore is found to be {eq}0.0095 \ \% {/eq} silver and {eq}0.036 \ \% {/eq} copper. What is the percentage of matter that is neither silver or copper?

Mutually Exclusive Events:

The complement rule for calculating probabilities states that: {eq}P(\overline{A})=1-P(A) {/eq}

Additionally, the rule of addition is written as: {eq}P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B) {/eq}

In the event that the events are mutually exclusive, {eq}P(A\bigcap B)=0 {/eq}, thus:

{eq}P(A\bigcup B)=P(A)+P(B) {/eq} for mutually exclusive events.

Answer and Explanation:

{eq}P(Ag)=0.000095 {/eq}

{eq}P(Cu)=0.00036 {/eq}


We know that {eq}P(Ag\bigcup Cu)=P(Ag)+P(Cu)-P(Ag\bigcap Cu) {/eq}

Since the events are mutually exclusive:

{eq}P(Ag\bigcap Cu)=0 {/eq}, therefore:

{eq}P(Ag\bigcup Cu)=P(Ag)+P(Cu) {/eq}

Replacing values:

{eq}P(Ag\bigcup Cu)=0.000095+0.00036\\ P(Ag\bigcup Cu)=0.000455 {/eq}

The required probability is:

{eq}P(\overline{Ag\bigcap Cu})=1-P(Ag\bigcup Cu)\\ P(\overline{Ag\bigcap Cu})=1-0.000455\\ P(\overline{Ag\bigcap Cu})=0.999545\\ {/eq}

The percentage of matter that is neither silver or copper is 99.9545.


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Mutually Exclusive Events & Non-Mutually Exclusive Events

from 6th-8th Grade Math: Practice & Review

Chapter 48 / Lesson 5
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