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Which pairs of events describe independent events? Select all that apply.

O Rolling a six-sided die and having it land on a 4, and then choosing a blue marble from a jar of marbles.

O Rolling a six-sided die and having it land on a 3,
and then rolling a six-sided die and having it land on a 2.

O Choosing a blue marble from a jar of marbles, not replacing it, and then drawing a red marble.

O Entering a raffle 3 times and winning one prize, and then winning another prize in the same raffle.

O Drawing a 3 from a deck of cards, not replacing it, and then drawing a 4 from the same deck of cards.

Respuesta :

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct options are A and B.

Which pair of events are called independent events?

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent iff we have:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Comparing it with chain rule will give

[tex]P(A|B) = P(A)\\P(B|A) = P(B)[/tex]

Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).

Two events are known to be independent even if the result of one event does not affect the result of the second event.

Rolling a dice in an independent event and choosing a blue marble is another independent event. The two events are independent and the result of one does not affect the other.

Thus, A is correct.

Rolling a dice in an independent event, and rolling it again won't affect the result of the second roll. Therefore, rolling a dice twice or for n number of times is an independent event.

Thus, B is correct.

Hence, the correct options are A and B.

Learn more about Independent Events:

brainly.com/question/1210781

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