We are give the following table of information:
`|[,"Deg. In","Deg. Out","Total"],["Male",192107,623018,815125],["Female",149091,909741,1058832],["Total",341198,1532759,1873957]|`
(a) We are asked to find P(Male or Deg. In).
We can use the addition rule P(A or B)=P(A)+P(B)-P(A and B) when A and B are not mutually exclusive. Here, it is possible for a male to receive a...
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degree in the field, so the characteristics are not mutually exclusive.
`P("MorDegIn")=815125/1873957+341198/1873957-192107/1873957=964216/1873957~~.5145` Another approach is to use the definition of probability: the number of items in the event space divided by the number of items in the sample space.
Here, the event space has males and people with degrees in the field, which is 192107+623018+149091=964216, and the sample space is 1873957.
(b) We are asked to find the probability that a randomly chosen person is female or has a degree outside the field, or P(F or Deg Out).
As above, we use the addition rule to get:
`P("ForDegO")=1058832/1873957+1532759/1873957-909741/1873957=1681850/1873957~~.8975` Again, we could find the size of the event space: 149091+909741+623018=1681850, as above.
(c) We are asked to find the probability that a randomly chosen person is not female or received a degree outside the field. We want `P(not"Female" " or Degree Out")` (This is different from `not("Female or Deg Out")` ; be careful of the wording.)
`not "Female"="Male"` for the sake of this table, so we get
`815125/1873957+1532759/1873957-623018/1873957=1724866/1873957~~.9204`.