Can the represent measures of probability ?
P(A$\cap$B) = 0.1, P(B) = 0.4, P( C) = 0.5
where A$\cup$ B$\cup$ C = S is the sure event and A,B,C are mutually exclusive.Solution in Bengali

If S is the sure event then-

Describe 'mutually exclusive' and 'mutually exhaustive' events and give examples with the help of a sample space.

Consider the line $l:\overrightarrow{r}=\hat{i}-\hat{j}+\hat{k}+t(2\hat{i}+3\hat{j}-6\hat{k})$ and the plane $p:\overrightarrow{r}.(2\hat{i}+3\hat{j}-6\hat{k})=7$.
Statement -I : Then line $l$ and the plane 'p' meet in a unique point .
Statement -II: The line $l$ is at right angoles to the plane 'p'

Let $\overrightarrow{a}=\hat{i}+\hat{j}-3\hat{k}\text{and}\overrightarrow{b}=2\hat{i}+\hat{j}+\hat{k}$
Statement - I: Vectors $\overrightarrow{a}\text{and}\overrightarrow{b}$ are perpendicular to each other
Statement - II: $\overrightarrow{a}.\overrightarrow{b}=0$

Let A, B and C be three events such that $P\left(A\right)=0.3,P\left(B\right)=0.4,P\left(C\right)=0.8,P(A\cap B)=0.08,P(A\cap C)=0.28,P(A\cap B\cap C)=0.09$. If $P(A\cup B\cup C)\ge 0.75$, then $P(B\cap C)$ satisfies

Can the represent measures of probability ?
P$\left(A\right)=0.4,P\left(A^c\right)$ = 0.52
where A$\cup$ B$\cup$ C = S is the sure event and A,B,C are mutually exclusive.

Can the represent measures of probability ?
P(A) = 0.38, P(B) = 0.30, P( C) = 0.32
where A$\cup$ B$\cup$ C = S is the sure event and A,B,C are mutually exclusive.

Can the represent measures of probability ?
P(A) = 0.5, P(B) = 0.4, P(B $\cup$ C) = 0.2
where A$\cup$ B$\cup$ C = S is the sure event and A,B,C are mutually exclusive.

Can the represent measures of probability ?
P(A$\cup$B) = 0.6, P(B) = 0.2, P( C) = 0.3
where A$\cup$ B$\cup$ C = S is the sure event and A,B,C are mutually exclusive.

The probabilities of three events A,B,C are P(A) = 0.6, P(B) = 0.4 and P( C) = 0.5.If P(A$\cup$B) = 0.8, P(A $\cap$C) = 0.3 , P(A$\cap B\cap$C) = 0.2 and P(A$\cup B\cup C$)$\ge$0.85, show that, 0.2$\le P(B\cap C)\le$ 0.35.

If the events A,B, and C are mutully exclusive then P(A$\cup B\cup C$) =

If the events A,B, and C are mutully exclusive then P(A$\cup B\cup C$) =

Can the following represent measures of probability :
P(A) = 0.2, P(B) = 0.7, P( C) = 0.1where (A$\cup$ B $\cup$ C ) represents sure event and A,B,C are mutually exclusive.

Can the following represent measures of probability :
P(A) = 0.4 , P(B) = 0.6 , P( C) = 0.2 where (A$\cup$ B $\cup$ C ) represents sure event and A,B,C are mutually exclusive.

Can the following represent measures of probability :
P(A $\cup$B) =0.5, P(B) = 0.6, P( C)= 0.2where (A$\cup$ B $\cup$ C ) represents sure event and A,B,C are mutually exclusive.