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there are five nickels and seven dimes in your pocket. four of the nickels and six of the dines are canadian. the others are US currency. you randomly select a coin from your pocket. what is the probability it is a nickel or it is Canadian currency?

Sagot :

We know that there are 5 nickels in total, and there are 10 Canadian currencies. We also know the total number of currencies is 12.

The probability of the event would be as not mutually exclusive events, which follows the following rule:

[tex]P(\text{AorB)}=P(A)+P(B)-P(AandB)[/tex]

The probabilities of A and B are

[tex]\begin{gathered} P(A)=\frac{5}{12} \\ P(B)=\frac{10}{12}=\frac{5}{6} \end{gathered}[/tex]

The probability of A and B is

[tex]P(\text{AandB)}=\frac{5}{12}\cdot\frac{5}{6}=\frac{25}{72}[/tex]

Then, we replace all these probabilities in the formula above.

[tex]P(\text{AorB)}=\frac{5}{12}+\frac{5}{6}-\frac{25}{72}=\frac{65}{72}\approx0.90[/tex]

Hence, the probability is around 90%.

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