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2 years ago

How are conditional probability and independent events related?

Mathematics

1 answer:

artcher [175]2 years ago

8 0

Answer:

1. P(A|B) - option 2

2. does not affect - option 2

3. P(A) - option 1

Step-by-step explanation:

By the definition, the notation P(A|B) reads the probability of event A given that event B has occured. So, for the first gap correct choice is 2 - P(A|B).

If events A and B are independent, then the probability of event B occuring does not affect the probability of event A occuring. So, for the second gap correct choice is 2 - does not affect.

Events A and B are independent, then

$P(A\cap B)=P(A)\cdot P(B)$

Use formula for the conditional probability:

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$

Since events A and B are independent, we get

$P(A|B)=\dfrac{P(A)\cdot P(B)}{P(B)}=P(A)$

So, for the third gap correct answer is 1 - P(A)

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The average lethal blood concentration of morphine is estimated to be 2.5 µg/mL with a standard deviation of 0.95 µg/mL. The dat

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2 years ago

If the area of the rectangle is 120, what is the area of triangle cpd

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Suppose that we want to investigate whether curfews correlate with differences in grades for students in middle school. We selec

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Answer:

Step-by-step explanation:

Hello!

Given the variables

X: Curfew of middle school students (Categorized Yes/No)

Y: Average grade of middle school students. (Categorized: A, B, C, and D)

The objective is to test if there is an association between both variables, you have to conduct a Chi-Square test of independence.

In the null hypothesis, you state that both variables are independent vs. the alternative hypothesis that the variables are dependent.

The hypotheses for this test are:

H₀: Pij= Pi. * P.j i= (1)Yes, (2)No; j= (1)A, (2)B, (3)C, (4)D

H₁: Te variables are not independent.

α: 0.05

$X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~X_{(r-1)*(c-1)}$

Where

Oij is the observed frequency for the i-row and j-column

Eij is the expected frequency for the i-row and j-column

r= number of categories in the rows

c= number of categories in the columns

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p-value: 0.687

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