Pregunta
- Question 1. If two evente are independent, the probability of both evente
happening is:
a) The sum of their individual probabilitien.
b) The difference of their individual probabilities.
c) The product of their individual probabilities.
d) Not related to their individual probabilitios.
happening is:
a) The sum of their individual probabilitien.
b) The difference of their individual probabilities.
c) The product of their individual probabilities.
d) Not related to their individual probabilitios.
Ask by West Campos. in the United States
Jan 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The probability of both independent events happening is the product of their individual probabilities.
Solución
To determine the probability of two independent events happening, we need to understand the definition of independent events in probability.
-
Independent Events: Two events
and are said to be independent if the occurrence of one does not affect the occurrence of the other. -
Probability of Independent Events: The probability of both events
and happening is given by the formula: whereis the probability of event occurring, and is the probability of event occurring.
Now, let’s analyze the options provided:
- a) The sum of their individual probabilities. (Incorrect)
- b) The difference of their individual probabilities. (Incorrect)
- c) The product of their individual probabilities. (Correct)
- d) Not related to their individual probabilities. (Incorrect)
Thus, the correct answer is:
c) The product of their individual probabilities.
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Simplifique esta solución Mind Expander
Did you know that the concept of independent events comes from the foundational work in probability theory by mathematicians like Pierre-Simon Laplace in the 18th century? Laplace helped formalize the idea that two events are independent if the occurrence of one does not affect the occurrence of the other – keeping the math community buzzing with excitement!
In real-world scenarios, independent events can be found all around us! For instance, consider flipping a fair coin and rolling a dice – the outcome of the coin flip doesn’t influence the numbers on the dice. This independence allows us to simply multiply their probabilities to get the likelihood of both happening! So, if you flip heads (1/2) and roll a six (1/6), the chance of both occurring simultaneously is (1/2) * (1/6) = 1/12!
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