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How would I write this event in set notation?

Suppose we have a random number generator which outputs integers between 1 and 100 inclusive ( such that P({1})=P({2})=P({100})=1/100)\left( \text{ such that } \mathbb{P}(\{1\})=\mathbb{P}(\{2\})=\mathbb{P}(\{100\})=1/100 \right).

Let AA be the event 'A multiple of 3 is generated.' How would I write that event?

Would it be A={3,6,9,...,93,96,99} A=\{3,6,9,...,93,96,99\} or A={{3},{6},{9},...{93},{96},{99}}? A=\{\{3\},\{6\},\{9\},...\{93\},\{96\},\{99\} \}?
(edited 6 years ago)
Reply 1
Avatar for B_9710
B_9710
18
Original post by Desmos
Suppose we have a random number generator which outputs integers between 1 and 100 inclusive (such that P(1)=P(2)=P(100)=1/100\mathbb{P} ({1})=\mathbb{P} ({2})=\mathbb{P} ({100})=1/100).

Let AA be the event 'A multiple of 3 is generated.' How would I write that event?

Would it be A=3,6,9,...,93,96,99 A={{3,6,9,...,93,96,99}} or A=3,6,9,...93,96,99? A={{{3},{6},{9},...{93},{96},{99}}}?

(The sets should have curly braces around them but it's not showing up)


The set would just be all multiples of 3 up to 100 as you've written.
Original post by Desmos
Suppose we have a random number generator which outputs integers between 1 and 100 inclusive (such that P(1)=P(2)=P(100)=1/100\mathbb{P} (\text{{}1\text{}})=\mathbb{P} ({2})=\mathbb{P} ({100})=1/100).

Let AA be the event 'A multiple of 3 is generated.' How would I write that event?

Would it be A=3,6,9,...,93,96,99 A=\text{{}3,6,9,...,93,96,99\text{}} or
Unparseable latex formula:

A=\text{{}\text{{}3\text{}},{6},{9},...{93},{96},{99}}}?



(The sets should have curly braces around them but it's not showing up)


The first one, A={3,6,9,...,93,96,99} A=\{3,6,9,...,93,96,99\}

The event A is a subset of your sample space.
(edited 6 years ago)
Original post by Desmos
Suppose we have a random number generator which outputs integers between 1 and 100 inclusive (such that P(1)=P(2)=P(100)=1/100\mathbb{P}({1})=\mathbb{P}({2})=\mathbb{P}({100})=1/100).

Let AA be the event 'A multiple of 3 is generated.' How would I write that event?

Would it be A=3,6,9,...,93,96,99 A={3,6,9,...,93,96,99} or
Unparseable latex formula:

A={{3}},{6},{9},...{93},{96},{99}}}?



(The sets should have curly braces around them but it's not showing up)


The first one.
(edited 6 years ago)
Reply 4
Avatar for MR1999
MR1999
OP
21
Thanks all, I get it now. :smile:

@NotNotBatman, @ghostwalker, @B_9710
(edited 6 years ago)
Reply 5
Avatar for MR1999
MR1999
OP
21
Original post by ghostwalker
The first one, A={3,6,9,...,93,96,99} A=\{3,6,9,...,93,96,99\}

The event A is a subset of your sample space.


Just another quick question: Is the way I wrote the probabilities correct? (It's different in the main post.)
Original post by Desmos
Just another quick question: Is the way I wrote the probabilities correct? (It's different in the main post.)


Yes.

If X={4}, for example, then P(X)=P({4})=1/100

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