Pregunta
- Question 2. Two events are independent if:
a) They have no outcomes in common.
b) The occurrence of one does not affect the occurrence of the other.
c) They both have the same probability of occurring.
d) They can never occur at the same time.
a) They have no outcomes in common.
b) The occurrence of one does not affect the occurrence of the other.
c) They both have the same probability of occurring.
d) They can never occur at the same time.
Ask by Klein Dickson. in the United States
Jan 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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Independent events are when the occurrence of one event does not affect the occurrence of the other.
Solución
To determine which statement correctly defines independent events, let’s analyze each option:
a) They have no outcomes in common.
This statement describes mutually exclusive events, not independent events. Independent events can have outcomes in common.
This statement describes mutually exclusive events, not independent events. Independent events can have outcomes in common.
b) The occurrence of one does not affect the occurrence of the other.
This is the correct definition of independent events. If two events are independent, knowing that one event occurred does not change the probability of the other event occurring.
This is the correct definition of independent events. If two events are independent, knowing that one event occurred does not change the probability of the other event occurring.
c) They both have the same probability of occurring.
This statement is not true for independent events. Independent events can have different probabilities.
This statement is not true for independent events. Independent events can have different probabilities.
d) They can never occur at the same time.
This statement also describes mutually exclusive events. Independent events can occur simultaneously.
This statement also describes mutually exclusive events. Independent events can occur simultaneously.
Based on this analysis, the correct answer is:
b) The occurrence of one does not affect the occurrence of the other.
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Simplifique esta solución Bonus Knowledge
Independent events are like two dancers at a party who don’t step on each other’s toes! This means that the outcome of one event does not influence the other; you could flip a coin while rolling a dice, and the results won’t affect each other one bit. So, if it’s heads for the coin, it’s still a free-for-all for the dice!
A classic example of independent events is flipping a coin and rolling a die. No matter if you get heads or tails on the coin, the die can still land on any of its six faces, totally untouched by the coin flip. So if you want a fun game, just throw those coins and dice around!
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