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Ray Of Light [21]
3 years ago
15

The probability of event A is x, and the probaility of event B is y.

Mathematics
2 answers:
kozerog [31]3 years ago
7 0
If an event is independent, it means other events have no effect<span> on this event.

So this means P(A | B) = P(A) because A and B are independence thus event B does not change anything regarding event A.

Hope this helps.</span>
stepladder [879]3 years ago
5 0

Answer:

The condition P(A|B) = x is true.

Step-by-step explanation:

Given : The probability of event A is x, and the probability of event B is y.

If the two events are independent.

To find : Which condition must be true?  

Solution :

P(A)=x and P(B)=y

If two events are independent

Then P(A\cap B)=P(A)\times P(B)

The formulas for conditional probabilities are

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

If we substitute the independent condition in conditional probability formulas we get,

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

Applying the given condition,

P(A/B)=P(A)=x\\\\P(B/A)=P(B)=y

Therefore, The condition P(A|B) = x is true.

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A random sample of 49 measurements from one population had a sample mean of 15, with sample standard deviation 5. An independent
kotykmax [81]

Answer:

Comparing the p value with the significance level \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the difference between the two groups is significantly different.  

Step-by-step explanation:

\bar X_{1}=15 represent the mean for sample 1

\bar X_{2}=18 represent the mean for sample 2

s_{1}=5 represent the sample standard deviation for 1  

s_{f}=6 represent the sample standard deviation for 2  

n_{1}=49 sample size for the group 2  

n_{2}=64 sample size for the group 2  

\alpha=0.01 Significance level provided

t would represent the statistic (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the difference in the population means, the system of hypothesis would be:  

Null hypothesis:\mu_{1}-\mu_{2}=0  

Alternative hypothesis:\mu_{1} - \mu_{2}\neq 0  

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:  

t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

And the degrees of freedom are given by df=n_1 +n_2 -2=49+64-2=111  

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:  

t=\frac{(15-18)-0}{\sqrt{\frac{5^2}{49}+\frac{6^2}{64}}}}=-2.897

P value

Since is a bilateral test the p value would be:  

p_v =2*P(t_{111}  

Comparing the p value with the significance level \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the difference between the two groups is significantly different.  

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3 years ago
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