Answer:
Option B) and option D) are independent events. i.e. following events are independent events:
- B) A coin is flipped and a spinner is spun
- D) Four number cubes are rolled at the same time.
Step-by-step explanation:
Two events would be termed as Independent events if the occurrence of one event would not affect the occurrence of other event.
Let us first consider the options having independent events.
- B) A coin is flipped and a spinner is spun
- D) Four number cubes are rolled at the same time.
Option B) i.e. 'a coin is flipped and a spinner is spun' is treated as neither of the events is affecting the outcome of other event. For example, assuming a coin and spinner are kept isolated, the occurrence of event of a flipping coin is not affecting the outcome of the occurrence of spinner.
The same goes with the option D) i.e. 'four number cubes are rolled at the same time', as neither of the rolling is affecting the rolling of other coin.
Now, let us consider the options having dependent events
- A) One ball is drawn from a bag of balls after another ball is drawn without replacement.
- C) White marbles are drawn from a bag of marbles without replacing the marbles.
Let us suppose one ball is drawn from a bag of balls after another ball is drawn without replacement. If there is no replacement, it logically means, after every drawn event, total number of the balls are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event. Hence, the occurrence of every event depends upon the occurrence of other event, meaning the two events will keep affecting the outcome if no replacement is made before the next event.
The same logic goes with when white marbles are drawn from a bag of marbles without replacing the marbles. If there is no replacement, it logically means, after every drawn event, total number of the white marbles and marbles are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event.
So, after all the discussion, we can safely say make a conclusion that option B) and option D) are independent events. i.e. following events are independent events:
- B) A coin is flipped and a spinner is spun
- D) Four number cubes are rolled at the same time.
Keywords: dependent events, independent events
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