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April 11th, 2017, 05:43 AM  #1 
Member Joined: May 2015 From: Australia Posts: 61 Thanks: 7  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 05:55 AM. 
April 11th, 2017, 07:18 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 740 Thanks: 208 
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 07:27 AM. 
April 11th, 2017, 07:37 AM  #3  
Senior Member Joined: May 2016 From: USA Posts: 904 Thanks: 359  Quote:
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.  
April 11th, 2017, 09:45 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 740 Thanks: 208 
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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determining, events, exclusive, mutually, probability 
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