# The accompanying table shows the numbers of male and female students in a certain region who received bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts (a) through (c). Use the table below. Degree in Field, Degree Outside of Field, Total. Males: 192107, 623018, 815125. Females: 149091, 909741, 1058832. Total: 341198, 1532759, 1873957. (a) The student is male or received a degree in the field. (b) The student is female or received a degree outside of the field. (c) The student is not female or received a degree outside of the field. Please put answers in the form of fractions and decimals.

(1) The probability of male or a degree in the field is 964216/1873957, or about .5145.
(2) The probability of female or a degree outside the field is 1681850/1873957, or about .8975.
(3) The probability of being not female or degree outside the field is 1724866/1873957, or about .9209.

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`.