Question

Think about Digit's game, spinning a spinner that is divided into 12 equally sized sections. Which option(s) represent(s) a pair of complementary events in this situation? 1) H=x:x is cured pasta & bear and Sc=x:x is not cooked mushroom & garlic chicken 2) R=x:x is oven-baked apple & lavender calzone and B=x:x is cured pasta & bear, cucumber & lime mutton, poached fennel & lemon alligator, pressure-cooked mushroom & garlic chicken, gooseberry & passion fruit cheesecake, or a praline wafer 3) F=x:x is pressure-cooked mushroom & garlic chicken and Fc=x=x:x is not pressure-cooked mushroom & garlic chicken 4) K=x:x is cucumber & lime mutton and F=x:x is a praline wafer 5) H=x:x is cured pasta & bear and S=x:x is cooked mushroom & garlic chicken

Answer 1

In the list of options given in the question, only the third option represents a pair of complementary events. This is because getting a pressure-cooked mushroom & garlic chicken and not getting a pressure-cooked mushroom & garlic chicken covers all the possible outcomes when spinning the Spinner.

Step-by-step explanation:

The subject of the question falls under the domain of probability theory. When considering the spinner divided into 12 equal parts, we need to understand the concept of complementary events. In probability, two events are said to be complementary if one event happens, the other does not. So, the sum of their probabilities is always 1. In the options given in the question, only the third option: F=x: x is pressure-cooked mushroom & garlic chicken and Fc=x: x is not pressure-cooked mushroom & garlic chicken denotes a pair of complementary events. Here, the event 'F' is getting a pressure-cooked mushroom & garlic chicken, and the event 'Fc' is not getting a pressure-cooked mushroom & garlic chicken. So either you will get a pressure-cooked mushroom & garlic chicken or not, which covers all possibilities when spinning the spinner, hence they are complementary.

Learn more about Complementary Events