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MTEL General Curriculum Mathematics Practice

Question 1

What is the probability that two randomly selected people were born on the same day of the week?  Assume that all days are equally probable.

A
\( \large \dfrac{1}{7}\)
Hint:
It doesn't matter what day the first person was born on. The probability that the second person will match is 1/7 (just designate one person the first and the other the second). Another way to look at it is that if you list the sample space of all possible pairs, e.g. (Wed, Sun), there are 49 such pairs, and 7 of them are repeats of the same day, and 7/49=1/7.
B
\( \large \dfrac{1}{14}\)
Hint:
What would be the sample space here? Ie, how would you list 14 things that you pick one from?
C
\( \large \dfrac{1}{42}\)
Hint:
If you wrote the seven days of the week on pieces of paper and put the papers in a jar, this would be the probability that the first person picked Sunday and the second picked Monday from the jar -- not the same situation.
D
\( \large \dfrac{1}{49}\)
Hint:
This is the probability that they are both born on a particular day, e.g. Sunday.
Question 1 Explanation: 
Topic: Calculate the probabilities of simple and compound events and of independent and dependent events (Objective 0026).
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