Which of the following statements is TRUE about the odds? Odds varies from zero to plus infinity. Odds is 1 when the probability is 50%. Odds is commonly expressed as the likelihood of an event occurring. All of the above

Which of the following statements is TRUE about the odds? Odds varies from zero to plus infinity. Odds is 1 when the probability is 50%. Odds is commonly expressed as the likelihood of an event occurring. All of the above

Expert's Answer

In this question, we are given three statements over here and we are to figure out which of the statements, is that true now? It's the statements about odds. So let's look at odds now four an event for means for events. Success, Okay, you can put here event success will be defined as the chance for the success divided by the chance against the success. Now suppose if I let P. B the chance for success means probability of success for the event, then one -P will be the probability of against the success or what we call failure. So what's is transfer success means P Divided by chance against success which is one -P. I can see from here, it's definitely gonna be a fraction number Greater, it goes to zero and less than equals to one. So the first statement says that odds varies from zero to plus infinity. Now in this case it's not correct. You can see that the upper bound here is one, it's not plus infinity. So this statement is false key. The second statement says that God is one when probability is 50%. Okay, let's take a look, I'm going to let the probability P b 0.5, that is 50%. So what's it's gonna be P over one minus P. So that will be 0.5 over 1 -0.5 and that is one. So this statement here is true. Okay, that statement odds is commonly expressed as the likelihood of an event occurring. Now that's not true because odds is defined to be the chance for success. That means the likelihood event occurring divided by chance against success, divided by the likelihood of the event not occurring, so it's not defined as the likelihood have been event occurring, so this statement is false.

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