Question

In A Survey Of 400 Students In A School , 100 Were Listed As Taking Apple Juice , 150 As Taking Orange Juice And 75 Were Listed As Taking Both Apple As Well As Orange Juice. Find How Many Students Were Taking Neither Apple Juice Nor Orange Juice.​

Answer 1

Answer:

Step-by-step explanation:

number of students taking apple juice = n(A) =100

number of students taking orange juice = n(O) = 150

number of students taking both = n(A ∩O) =75

number of students taking either apple or orange juice = n(A∪O)

n(A∪O) = n(A)+n(O)-n(A∩O)

=100+150-75

=100+75

=175

Answer 2

$\fbox{ \fbox{ \bold{ \huge{Given :- \: }}}}$

$\to \: \bold{n ( U ) = 400 \: } \\ \to \: \bold{n ( A ) = 100 \: } \\ \to \: \bold{n ( O ) = 150 \: } \\ \to \: \bold{n ( A \: Π \: O ) = 75 \: }$

$\fbox{ \fbox{ \bold{ \huge{To \: Find :- \: }}}}$

$\to \: \bold{n ( A \: U \: O )' = \: ?}$

$\fbox{ \fbox{ \bold{ \huge{Solution :- \: }}}}$

$\bold{ \implies \: \underline{ \large{n ( A \: U \: O ) \: }}}$

$\to \bold{n ( A \: U \: O ) = n ( A ) + n ( O ) - n ( A \: Π \: O )</p><p> \: } \\ \to \bold{n ( A \: U \: O ) = 100 + 150 - 75 } \\ \to \bold{n ( A \: U \: O ) = 250 - 75 } \\ \to \bold{n ( A \: U \: O ) = 175</p><p> \: }$

$\bold{ \implies \: \underline{ \large{n ( A \: U \: O )' \: }}}$

$\to \bold{n ( A \: U \: O )' = n ( U ) - n ( A \: U \: O ) \: } \\ \to\bold{n ( A \: U \: O )' = 400 - 175} \\ \to\bold{n ( A \: U \: O )' = 225}$

$\bold{ \underline{ \large{Hence \: ， \: 225 \: Students \: Were \: Taking \: Neither \: Apple \: Juice \: Nor \: Orange \: Juice }}}$