# A middle school assigned a four digit ID number to each student. The number is made from the digits 123 and four and no digit is repeated if assigned randomly, what is the probability that an ID number will end with the number three

Question
Factors and multiples
A middle school assigned a four digit ID number to each student. The number is made from the digits 123 and four and no digit is repeated if assigned randomly, what is the probability that an ID number will end with the number three

2020-11-04
If the last digit must be a 3 and no digit can repeat, then there are 3 options (1, 2, and 4) for the first digit, 2 options for the second digit, 1 option for the third digit, and 1 option (a 3) for the last digit. The total number of outcomes that end with the number three is then $$\displaystyle{3}\times{2}\times{1}\times{1}={6}.$$
The total number of possible outcomes is $$\displaystyle{4}\times{3}\times{2}\times{1}={24}$$ since there are 4 options for the first digit, 3 for the second, 2 for the third, and 1 for the fourth.
The probability an ID number will end with the number three is then PSK\frac{6}{24}=\frac{1}{4}

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State the null and alternate hypotheses.
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}$$
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations,
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,
The Student's t. We assume that both population distributions are approximately normal with known standard deviations,
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimalplaces.)
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value $$\displaystyle>{0.250}$$
$$\displaystyle{0.125}<{P}-\text{value}<{0},{250}$$
$$\displaystyle{0},{050}<{P}-\text{value}<{0},{125}$$
$$\displaystyle{0},{025}<{P}-\text{value}<{0},{050}$$
$$\displaystyle{0},{005}<{P}-\text{value}<{0},{025}$$
P-value $$\displaystyle<{0.005}$$
Sketch the sampling distribution and show the area corresponding to the P-value.
P.vaiue Pevgiue
P-value f P-value