I have two main questions. 1. In a survey conducted by Helena, a financial consu
ID: 3108628 • Letter: I
Question
I have two main questions.
1. In a survey conducted by Helena, a financial consultant, it was revealed of her 405 clients:
276 own stocks.
192 own bonds.
175 own mutual funds.
116 own both stocks and bonds.
106 own both stocks and mutual funds.
102 own both bonds and mutual funds.
How many of Helena's clients own stocks, bonds, and mutual funds? (Assume each client invested in at least one of the three types of funds.)
2. The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 510 graduates
200 had at least one year of Spanish.
170 had at least one year of French.
141 had at least one year of German.
43 had at least one year of Spanish and French.
26 had at least one year of Spanish and German.
22 had at least one year of French and German.
3 had at least one year of all three languages.
(a) How many of the graduates had at least 1 yr of at least one of the three languages?
(b) How many of the graduates had at least 1 yr of exactly one of the three languages?
(c) How many of the graduates had less than 1 yr of any of the three languages?
Explanation / Answer
1)
Given that
n( S u B u M ) = 405
n(S) = 276 , n( B) = 192 n (M ) =175
n ( S ^ B ) = 116 n( S ^ M )= 106 n( B ^ M ) =102
n ( S ^ B ^ M ) = ?
We know that from set theory
n( S u B u M ) = n(S) + n( B) +n (M ) - n ( S ^ B ) - n( S ^ M )= 106 - n( B ^ M ) + n ( S ^ B ^ M )
405= 276 + 192 + 175 - 116 -106 - 102 + n ( S ^ B ^ M )
n ( S ^ B ^ M ) = 405- 319 = 86
2)
a)
n(S) =200 , n( F) =170 n(G) =141
n( S ^ F ) = 43 n( S ^ G ) = 26 n( F ^ G )= 22 n ( S ^ F ^ G )= 3
n( S u F u G ) = n( S ) + n( F ) + n ( G ) - n( S^ F) - n( S ^ G ) - n( F ^ G ) + n( S ^ F ^ G )
= 200 + 170 + 141 -43 -26 - 22+ 3 = 423
423 student had at lest 1 year of atleast one of the subject
c ) no of student had less than 1 year of any of three languages= Total student - 423 = 510 - 423 = 87