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April 11th, 2017, 04:43 AM   #1
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Determining probability of mutually exclusive events

“ A fair 20 sided die is numbered 1 to 20. Write down at least eight pairs of mutually exclusive events related to this die. Determine their probabilities ”

I dont know what the answer is.
So far, I think what they mean is, for example, Pr(6 and 8 )= 0

i think the probability is 0 because rolling a 6 and an 8 at the same time is impossible on the same die. I'm assuming there is only one die.

Or should i write it as Pr(6 or 8 )=2/20=1/10

I'm not exactly sure what the answer is. If someone could help, i'd greatly appreciate it!

Last edited by pianist; April 11th, 2017 at 04:55 AM.
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April 11th, 2017, 06:18 AM   #2
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Given that any number between 1 and 20 can result and using your imagination, you can come up with lots of possible events, that have a pairing, apart from the obvious "The number 1 v any other number".

A number > 10

An odd number

A number divisible by 3

A single digit number.

The result is a perfect square

The number of dollars you will give me for helping...

Taking your example

The probability of a 6 is 1/20 ie P(E | 6) = 1/20 So the probability of P(E | not6) = (1 -1/20) = 19/20

Note the probability of E being 6 or 8 is still one event with a probability of 2/20 so by itself is not a complete answer,
but (E | 6) and (E | 8 ) are mutually exclusive possible outcomes each with a probability of 1/20

Last edited by studiot; April 11th, 2017 at 06:27 AM.
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April 11th, 2017, 06:37 AM   #3
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Quote:
Originally Posted by pianist View Post
“ A fair 20 sided die is numbered 1 to 20. Write down at least eight pairs of mutually exclusive events related to this die. Determine their probabilities ”

I dont know what the answer is.
So far, I think what they mean is, for example, Pr(6 and 8 )= 0

i think the probability is 0 because rolling a 6 and an 8 at the same time is impossible
It is a very badly worded question. What does "their" refer to, the 8 pairs or the 16 events?

The probability of two mutually exclusive events happening simultaneously is, as you correctly saw, zero. So if the problem is asking for those probabilities, you simply write down 0 eight times. I suspect, however, that you are being asked to find the probabilities of each event in each pair that you list.
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April 11th, 2017, 08:45 AM   #4
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I think one of the teaching points of this question is that events can be either simple of compound.

S = the sample space, the set of all possible outcomes of the experiment.

S = {1,2,3....19,20}

An event is any set of possible outcomes. The event set is a subset of S

A simple event is a single outcome - a subset of S with precisely one element.
eg a 6 is rolled,

or they can be compound events such as either 6 or 8 is rolled or an odd number is rolled,
in which case the event is the set {6,8}.
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