Question

For an event, odds against is 6 : 5, the probability that event does not occur is:
1. $\dfrac{5}{6}$
2. $\dfrac{6}{11}$
3. $\dfrac{5}{11}$
4. $\dfrac{1}{6}$

Answer 1

Hint: For solving this question you should know about the concept of probability. In this question we will first calculate all the possibilities which are possible according to our question and that will be our complete result and then from that we will select our requirement. And at last we will take care of both results. That will be our final answer.

Complete step-by-step solution:
So, as we know that according to the concept of probability it is clear that the probability cannot be greater than one ever. And this is always fixed. So, the probability of any event is always less than or equal to one. And thus the probability is defined. If the probability of any event to occur is x, then the probability of that event not to occur is always 1 - x, because the total of both or all the probabilities for an event is always equal to one.
So, if we use the concept of probability here, then, total cases are = 6 + 5 = 11.
And it is given that, odd against is = 6 : 5.
Hence the probability of the event not occurring is,
$P\left( E' \right)=\dfrac{6}{11}$
Hence the correct option is 2.

Note: For solving these types of questions, always understand the condition clearly. If the conditions will not be clear, then these will give us the wrong answer. And count every single term according to the given conditions and if any term is left then the probability will be wrong and that will be the wrong answer.