Q1 Q2 Among 123 people interviewed as part of an urban mass

Q1:

Q2:

Among 123 people interviewed as part of an urban mass transportation study, some live more that 4 miles from city center (A), some regularly drive to work (B), and some would like to switch to public mass transportation if it was available (C). Use the information provided by the below Venn diagram (the numbers are the counts of people that fall into each given region) to find 17 4 35 16 18 (a) P(B) (b) P(Bnc) (c) P(AUC) (d) P(An (BnC\')) (e) P(A\'U B\'UC) (f) P([Bnc\'n[AUuC)

Solution

There are 123 people here.

Thus,

a)

Adding all terms inside circle B then dividing by 123,

P(B) = (17 + 4 + 35 + 16) / 123 = 0.585365854 [answer]

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b)

Adding all terms inside circle B and C then dividing by 123,

P(B U C) = (17 + 4 + 35 + 16 + 22 + 8) / 123 = 0.829268293 [answer]

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c)

Adding all terms inside circle A and C then dividing by 123,

P(B U C) = (3 + 17 + 35 + 16 + 22 + 8) / 123 = 0.821138211 [answer]

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d)

Here,

n(B n C\') = 17 + 4 = 21

Of which, only the 17 part is intersected by A,

n(A n (B n C\')) = 17

Thus,

P(A n (B n C\')) = 17/123 = 0.138211382 [answer]

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