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There are $W \,,X\,, Y\,, \& Z$ possible activities a nurse can carry out whilst on a shift. Whilst observing n nurses, $W \,,X\,, Y\,, \& Z$ happened $w$% $x$% $y$% and $z$% of the time respectively. However since w+x+y+z sums to more than 100% then some nurses do more than one task at a time. We know that the probability of doing: 1 activity =63.8%, 2 activities =30%, 3 activities =6% 4 activities= 0.2%

Is it possible to calculate the probability of doing activity X? or is more information needed?

Thank you, and please ask for clarification is this is unclear. Best regards.

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    @user1134241 In this case, either you just care about the probability of doing x, which is x%, as Dan mentioned first, or you care about the probability of doing X alone, which x/100 * 0.638. EDIT: unless you mean the probability of doing X w.r.t. Y, W and Z, and not the probability of doing X during a shift. In which case, Dan's answer seems correct.2012-01-24

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It can't be estimated from the data since there is no information about which activities are taking place. For example, it may be that X alone is active 64% of the time, Y & Z alone are active 30% of the time, Y & Z & W alone are active 25% of the time, and all four are active 1% of the time, in which case X is active 65% of the time (64% + 1%), because these events are mutually exclusive. But if we swap e.g. X and W we get a different answer. So more information is needed.

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    @user1134241, consider accepting my answer and posting that as a new question? This comment thread is getting too long.2012-01-24