Respuesta :
A number cube being rolled and a spinner being spun, two cards chosen from a deck and being replaced, a card being chosen and a dark randomly thrown- these are all examples of independent events because one outcome did not effect the outcome of the other event. And in the case of the cards, because it was replaced, each card still had exactly the same probability of being drawn.
Independent events don't affect each other. The options that show that the two events are independent are B, C, and E.
What are independent events?
Two events are known to be independent events if the occurrence of one doesn't affect another.
A.) Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number.
In the above problem after picking up a number Sarah keeps it, later on, Sarah picks up another number, therefore, in the second chance, the total possible outcomes are reduced.
Thus, the two events are not independent events.
B.) A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner.
We know that rolling a cube and a spinner are two different events, and the occurrence of one won't affect the other.
Thus, the two events are independent events.
C.) Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card
In the given option after choosing a card, Eliza keeps the card back in the deck, therefore, the number of possible outcomes is the same which will not affect the second event.
Thus, the two events are independent events.
D.) Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair.
In the given option after choosing a pair of socks from the drawer, the number of choices of socks that can be chosen from the drawer reduces.
Thus, the two events are not independent events.
E.) A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s eye.
In the given option picking up a card from the deck, and throwing a dart are the two different events and they won't affect each other.
Thus, the two events are independent events.
Hence, the options that show that the two events are independent are B, C, and E.
Learn more about Independent Events:
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