Recent questions tagged conditional-probability / GATE Overflow for GATE CSE

16 votes

2 answers

31

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 3
Suppose that $k$ events $B_1, B_2, \ldots, B_k$ form a partition of the sample space $S$. There is another event $A$ that $\operatorname{Pr}(A)>0.$ Which of the following is/are CORRECT? $\sum_{i=1}^k P\left(B_i\right)=1$ ... $\sum_{i=1}^k P\left(A \mid B_i\right)=1$ $\sum_{i=1}^k P\left(B_i \wedge A\right)=P(A)$

Suppose that $k$ events $B_1, B_2, \ldots, B_k$ form a partition of the sample space $S$. There is another event $A$ that $\operatorname{Pr}(A)>0.$Which of the following ...

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GO Classes asked Apr 12, 2023

14 votes

2 answers

32

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 4
$A$ and $B$ are two events. If $P(A, B)$ decreases while $P(A)$ increases, what must be true: $P(A \mid B)$ decreases $P(B \mid A)$ decreases $P(B)$ decreases All of above

$A$ and $B$ are two events. If $P(A, B)$ decreases while $P(A)$ increases, what must be true:$P(A \mid B)$ decreases$P(B \mid A)$ decreases$P(B)$ decreasesAll of above

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GO Classes asked Apr 12, 2023

11 votes

3 answers

33

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 6
Which of the following(s) expression is/are the same as $P(A, B, C)$ given no independent assumptions? $P(C \mid A, B) \cdot P(A, B)$ $P(C \mid A, B) \cdot P(A) \cdot P(B)$ $P(A \mid B) \cdot P(B \mid C) \cdot P(C)$ $P(A \mid B, C) \cdot P(B \mid C) \cdot P(C)$

Which of the following(s) expression is/are the same as $P(A, B, C)$ given no independent assumptions?$P(C \mid A, B) \cdot P(A, B)$$P(C \mid A, B) \cdot P(A) \cdot P(B)$...

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668 views

GO Classes asked Apr 12, 2023

13 votes

4 answers

34

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 7
Suppose we wish to calculate $P(H \mid E 1, E 2),$ and we have no conditional independence information. Which of the following sets of numbers are sufficient for the calculations? $P(E 1, E 2), P(H), P(E 1 \mid H), P(E 2 \mid H)$ $P(E 1, E 2), P(H), P(E 1, E 2 \mid H)$ $P(H), P(E 1 \mid H), P(E 2 \mid H)$ $P(H), P(E 1 \mid H)$

Suppose we wish to calculate $P(H \mid E 1, E 2),$ and we have no conditional independence information.Which of the following sets of numbers are sufficient for the calcu...

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700 views

GO Classes asked Apr 12, 2023

10 votes

2 answers

35

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 9
Which of the following statements is NOT true? If $A \subset B$, then $P(A) \leq P(B)$. If $P(B)>0$, then $P(A \mid B) \geq P(A)$. $P(A \cap B) \geq P(A)+P(B)-1$. $P\left(A \cap B^c\right)=P(A \cup B)-P(B)$.

Which of the following statements is NOT true?If $A \subset B$, then $P(A) \leq P(B)$.If $P(B)>0$, then $P(A \mid B) \geq P(A)$.$P(A \cap B) \geq P(A)+P(B)-1$.$P\left(A \...

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789 views

GO Classes asked Apr 12, 2023

13 votes

2 answers

36

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 10
I have two six-sided dice. The first die has $3$ faces painted red and the other $3$ painted black. The second has $1$ red face and $5$ black faces. When I roll a die, each of the six faces are equally likely. I choose a die at random ( ... given that the first roll came up $\text{ red"}$? $1 / 2$ $3 / 4$ $1 / 6$ $1 / 3$

I have two six-sided dice. The first die has $3$ faces painted red and the other $3$ painted black. The second has $1$ red face and $5$ black faces. When I roll a die, ea...

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GO Classes asked Apr 12, 2023

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