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.