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3 years ago

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In theoretical probability, what does it mean when the question asks ‘at least’, for example what is the probability of getting

at least a 2 when a six sided die is rolled?

1 answer:

klio [65]3 years ago

5 0

Answer:

Step-by-step explanation:

It means that you will a 2 or a 3 or a 4 or a 5 or 6.

All of these are permitted.

So the probability of getting at least a 2 is 5/6.

You might be interested in

The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed

algol [13]

Answer:

$\chi^2 = \frac{(27-33.33)^2}{33.33}+\frac{(31-33.33)^2}{33.33}+\frac{(42-33.33)^2}{33.33}+\frac{(40-33.33)^2}{33.33}+\frac{(28-33.33)^2}{33.33}+\frac{(32-33.33)^2}{33.33} =5.860$

$p_v = P(\chi^2_{5} >5.860)=0.32$

Since the p value is higher than the significance level assumed 0.05 we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we can assume that we have equally like results.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

Number: 1, 2 , 3 , 4 , 5 ,6

Frequency: 27, 31, 42, 40, 28, 32

We need to conduct a chi square test in order to check the following hypothesis:

H0: The outcomes are equally likely.

H1: The outcomes are not equally likely.

The level of significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The observed values are given:

$O_{1}=27$ $O_{2}=31$

$O_{3}=42$ $O_{4}=40$

$O_{5}=28$ $O_{6}=32$

The expected values are given by:

$E_{1} =\frac{1}{6}*200=33.33$ $E_{2} =\frac{1}{6}*200=33.33$

$E_{3} =\frac{1}{6}*200=33.33$ $E_{4} =\frac{1}{6}*200=33.33$

$E_{5} =\frac{1}{6}*200=33.33$ $E_{6} =\frac{1}{6}*200=33.33$

And now we can calculate the statistic:

$\chi^2 = \frac{(27-33.33)^2}{33.33}+\frac{(31-33.33)^2}{33.33}+\frac{(42-33.33)^2}{33.33}+\frac{(40-33.33)^2}{33.33}+\frac{(28-33.33)^2}{33.33}+\frac{(32-33.33)^2}{33.33} =5.860$

Now we can calculate the degrees of freedom for the statistic given by:

$df=Categories-1=6-1=5$

And we can calculate the p value given by:

$p_v = P(\chi^2_{5} >5.860)=0.32$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(5.860,5,TRUE)"

Since the p value is higher than the significance level assumed 0.05 we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we can assume that we have equally like results.

4 0

3 years ago

when Kaitlin divided a fraction by one half the result was a mixed number was the original fraction less than or greater than 1/

kramer

Greater!! ,because is a mix number...

5 0

3 years ago

Which set of whole numbers share the common multiples 2,520 and 3,780?

olya-2409 [2.1K]

The set of whole numbers that share the common multiples of 2,520 and 3,780 are: 35, 105, and 315.
To get these sets of whole numbers, you have to decompose 2520 and 3780 by using decomposition method or the continuous division.

See attached file.

7 0

3 years ago

Which equation shows that 6 is a factor of 18?

crimeas [40]

Since factors need to show that a number can be divided by another and 6*3=18, C is the answer.

7 0

3 years ago

Read 2 more answers

4−(3x−8)=21 solve this pls

riadik2000 [5.3K]

Answer:

4 - ( 3x - 8 ) = 21

break the bracket first ,it gives : 4 - 3x + 8 = 21

12 - 3x = 21

- 3x = 21 - 12

- 3x = 9

-x = 9/3

-x = 3

X = - 3

[ check if the answer is correct, put -3 instead of X in the above equation ! we get 4 - { 3(-3) - 8 } = 21

4 - { - 9 - 8 } = 21

4 - { - 17 } = 21

break the bracket, minus and minus will multiply and will become plus , so we have 4 + 17 = 21 , hence 21 = 21 ! therefore X = -3

5 0

2 years ago