Let ${E_1},{E_2},{E_3}$ be three arbitrary events of a sample space $S$. Consider the following statements which of the following statements are correct
Let ${E_1},{E_2},{E_3}$ be three arbitrary events of a sample space $S$. Consider the following statements which of the following statements are correct
- A
$P$ (only one of them occurs)
$ = P({\bar E_1}{E_2}{E_3} + {E_1}{\bar E_2}{E_3} + {E_1}{E_2}{\overline E _3})$
- B
$P$ (none of them occurs)
$ = P({\overline E _1} + {\overline E _2} + {\overline E _3})$
- C
$P$ (atleast one of them occurs)
$ = P({E_1} + {E_2} + {E_3})$
- D
$P$ (all the three occurs)$ = P({E_1} + {E_2} + {E_3})$
where $P({E_1})$denotes the probability of ${E_1}$ and ${\bar E_1}$ denotes complement of ${E_1}$.
Similar Questions
Fill in the blanks in following table :
$P(A)$
$P(B)$
$P(A \cap B)$
$P (A \cup B)$
$\frac {1}{3}$
$\frac {1}{5}$
$\frac {1}{15}$
........
Fill in the blanks in following table :
| $P(A)$ | $P(B)$ | $P(A \cap B)$ | $P (A \cup B)$ |
| $\frac {1}{3}$ | $\frac {1}{5}$ | $\frac {1}{15}$ | ........ |
Events $\mathrm{A}$ and $\mathrm{B}$ are such that $\mathrm{P}(\mathrm{A})=\frac{1}{2}, \mathrm{P}(\mathrm{B})=\frac{7}{12}$ and $\mathrm{P}$ $($ not $ \mathrm{A}$ or not $\mathrm{B})=\frac{1}{4} .$ State whether $\mathrm{A}$ and $\mathrm{B}$ are independent?
Events $\mathrm{A}$ and $\mathrm{B}$ are such that $\mathrm{P}(\mathrm{A})=\frac{1}{2}, \mathrm{P}(\mathrm{B})=\frac{7}{12}$ and $\mathrm{P}$ $($ not $ \mathrm{A}$ or not $\mathrm{B})=\frac{1}{4} .$ State whether $\mathrm{A}$ and $\mathrm{B}$ are independent?
Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac {1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is
Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac {1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is
- [JEE MAIN 2019]
The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject ............ $\%$
The chances to fail in Physics are $20\%$ and the chances to fail in Mathematics are $10\%$. What are the chances to fail in at least one subject ............ $\%$
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7 .$ The probability of passing at least one of them is $0.95 .$ What is the probability of passing both ?
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7 .$ The probability of passing at least one of them is $0.95 .$ What is the probability of passing both ?