Section B ( 41 marks )
7 . In a music class of 50 girls , 35 girls play guitar and 45 girls play violin . Each girl must play at least one musical instrument from guitar and violin .
( a ) ( i ) Find the number of girls who play both musical instruments .
( ii ) Hence , write down the number of girls who play guitar only .
( b ) One girl is selected at random .
[ 3 ]
( i ) Write down the probability that she plays violin .
( ii ) Given that the girl selected plays violin , find the probability that she also plays guitar .
[ 3 ]
Two girls are selected at random .
( c ) Find the probability that both girls play guitar only .
[ 2 ] Let G be the event that a girl plays guitar and V be the event that a girl plays violin .
( d ) Show that G and V are
( i ) not mutually exclusive ;
( ii ) not independent . [ 5 ]
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