If A and B are two events such that text{P}(text{A}|text{B})=text{p},text{P(A)}=text{p},text{P(B)}=frac{1}{3} and text{P}(text{A}cuptext{B})=frac{5}{9}, then p =

Q: If A and B are two events such that $\text{P}(\text{A}|\text{B})=\text{p},\text{P(A)}=\text{p},\text{P(B)}=\frac{1}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then p =

$\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P(A)}=\text{p},\text{P(B)}=\frac{1}{3},\text{P}(\text{A}\cup\text{B})=\frac{5}{9}$ Consider, $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p}$ $\Rightarrow \frac{\text{P}(\text{A}\cap\text{B})}{\text{P(B)}}=\text{P}$ $\Rightarrow \frac{\text{P(A)}+\text{P(B)}-\text{P}(\text{A}\cup\text{B})}{\text{P(B)}}=\text{P}$ $\Rightarrow\frac{\text{p}+\frac{1}{3}-\frac{5}{9}}{\frac{1}{3}}=\text{p}$ $\Rightarrow\text{p}+\frac{1}{3}-\frac{5}{9}=\frac{\text{p}}{3}$ $\Rightarrow\frac{-2}{9}=\frac{\text{p}}{3}-\text{p}$ $=\frac{-2}{3}\text{p}=\frac{-2}{9}$ $\Rightarrow\text{p}=\frac{1}{3}$

M.C.Q (1 Marks)

GSEB - English Medium

If A and B are two events such that $\text{P}(\text{A}|\text{B})=\text{p},\text{P(A)}=\text{p},\text{P(B)}=\frac{1}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then p =

A$\frac{2}{3}$
B$\frac{3}{5}$
C$\frac{1}{3}$
D$\frac{3}{4}$

STD 12 Science
Maths
Probability
Exemplar

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X:	1	2	3	4	5	6	7	8
P(X):	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

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