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Find the probability of rolling a number other than the number 1 when a die numbered 1-6 is rolled. P(not 1) P(odd number)

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Pauline Sheehan eNotes educator | Certified Educator

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As there are six possibilities and we are considering the probability of the outcome NOT being a number 1, or being an odd number (that is, 1,3,5)- then there are 5 other possibilities and 3 other possibilities respectively.

P (not 1) = `5/6`         or 5:6   or 83%

P (odd ) = `3/6=1/2`   or 1:2  or 50%     

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Tibor Pejić eNotes educator | Certified Educator

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First, `P(not 1)` this is probability of opposite event wich meens you should apply this formula: `P(not x)= 1-P(x)`. So since `P(x)= 1/6`

`P(not 1)= 1-P(x)= 1- 1/6= 5/6.`

Second, I belive this was supposed to be `P(odd number).` For odd number you have:

`P(odd number)= P({1,3,5})= P({1} bigcup {3} bigcup {5})= P(1)+ P(3)+ P(5)=` `1/6+ 1/6+ 1/6 = 3/6 = 1/2`

wihch is to be expected since you have equal number of odd and even numbers on rhe cube. Third equallity is valid because events of getting number 1, number 3 and number 5 are  mutually exclusive. For not mutally exclusive events A and B eg. `A = number geq 3` and `B = number leq 3` you would apply formula

`P(A bigcup B) = P(A) + P(B) - P(A bigcap B).`

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