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The probability of an event is 2/7. What are the odds of the same event?

A, 7/9
B, 5/7
C, 2/9
D, 2/5

Respuesta :

Answer:

D. [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Since we know that the odds of an events can be found by dividing the probability that an event will occur by the probability that the event will not occur.

[tex]\text{Odds of an event}=\frac{\text{Probability that event will occur}}{\text{Probability that event will not occur}}[/tex]

Probability of an event not occurring can be found by subtracting probability of the event occurring from 1.

[tex]\text{Odds of an event}=\frac{\text{Probability that event will occur}}{1-\text{Probability that event will occur} }[/tex]  

We have been given that probability of an event is 2/7.  

Upon substituting our given values in above formula we will get,

[tex]\text{Odds of the given event}=\frac{\frac{2}{7}}{1-\frac{2}{7}} }[/tex]

[tex]\text{Odds of the given event}=\frac{\frac{2}{7}}{\frac{7-2}{7}} }[/tex]

[tex]\text{Odds of the given event}=\frac{\frac{2}{7}}{\frac{5}{7}} }[/tex]

[tex]\text{Odds of the given event}=\frac{2}{7}\times \frac{7}{5}[/tex]

[tex]\text{Odds of the given event}=\frac{2}{5}[/tex]

Therefore, the odds of the same event are [tex]\frac{2}{5}[/tex] and option D is the correct choice.



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