Need help with this question, no need to mention the formula just need the reasoning.
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Need help with this question, no need to mention the formula just need the reasoning.
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Given that, In class XI of a school,
40% of the students study Mathematics
30% study Biology
10% of the class study both Mathematics and Biology.
Let assume that
A represents the set of students study Mathematics
B represents the set of students study Biology
So, According to statement
\begin{gathered}\sf \: P(A) = \dfrac{40}{100} \\ \\ \end{gathered}
P(A)=
100
40
\begin{gathered}\sf \: P(B) = \dfrac{30}{100} \\ \\ \end{gathered}
P(B)=
100
30
\begin{gathered}\sf \: P(A\cap B) = \dfrac{10}{100} \\ \\ \end{gathered}
P(A∩B)=
100
10
Now, we have to find the probability that he will be studying Mathematics or Biology.
We know,
\begin{gathered}\sf \: P(A\cup B) = P(A) + P(B) - P(A\cap B) \\ \\ \end{gathered}
P(A∪B)=P(A)+P(B)−P(A∩B)
So, on substituting the values, we get
\begin{gathered}\sf \: P(A\cup B) = \dfrac{40}{100} + \dfrac{30}{100} - \dfrac{10}{100} \\ \\ \end{gathered}
P(A∪B)=
100
40
+
100
30
−
100
10
\begin{gathered}\sf \: P(A\cup B) = \dfrac{40 + 30 - 10}{100} \\ \\ \end{gathered}
P(A∪B)=
100
40+30−10
\begin{gathered}\sf \: P(A\cup B) = \dfrac{60}{100} \\ \\ \end{gathered}
P(A∪B)=
100
60
\begin{gathered}\bf\implies \:60\% \: will \: be \: studying \: Mathematics \: or \: Biology \\ \\ \end{gathered}
⟹60%willbestudyingMathematicsorBiology
\rule{190pt}{2pt}
Additional Information :-
\begin{gathered}\boxed{ \sf{ \:P(A\cap B') = P(A) - P(A\cap B) \: }} \\ \\ \end{gathered}
P(A∩B
′
)=P(A)−P(A∩B)
\begin{gathered}\boxed{ \sf{ \:P(B\cap A') = P(B) - P(A\cap B) \: }} \\ \\ \end{gathered}
P(B∩A
′
)=P(B)−P(A∩B)
\begin{gathered}\boxed{ \sf{ \:P(B'\cap A') = 1 - P(A\cup B) \: }} \\ \\ \end{gathered}
P(B
′
∩A
′
)=1−P(A∪B)
\begin{gathered}\boxed{ \sf{ \:P(B'\cup A') = 1 - P(A\cap B) \: }} \\ \\ \end{gathered}
P(B
′
∪A
′
)=1−P(A∩B)