Dark Mode

Recent questions tagged goclasses2024_wq8

16 votes

3 answers

1

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 1
Which all of the following is true for the Venn diagram shown here: $P(E \cup G)=P(E)+P(G)$ $P(E \cup G)=P(E)+P(G)-P(E \cap G)$ $P\left(E^C \cap F\right)=P\left(F^C\right)-P(E)$ $P\left(E^C \cap F\right)=1-\left(P\left(F^C\right)-P(E)\right)$

GO Classes asked in Probability Apr 12, 2023

868 views

14 votes

2 answers

2

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 2
Which of the following is/are CORRECT? If events $E_1$ and $E_2$ are statistically independent, then $ \mathrm{P}\left(E_1 \cup E_2\right)=\mathrm{P}\left(E_1\right)+\mathrm{P}\left(E_2\right) $ If events $E_1$ and $E_2$ are ...

GO Classes asked in Probability Apr 12, 2023

931 views

14 votes

2 answers

3

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? $\sum_{i=1}^k P\left(B_i\right)=1$ ... $\sum_{i=1}^k P\left(A \mid B_i\right)=1$ $\sum_{i=1}^k P\left(B_i \wedge A\right)=P(A)$

GO Classes asked in Probability Apr 12, 2023

1.0k views

12 votes

2 answers

4

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

GO Classes asked in Probability Apr 12, 2023

1.2k views

18 votes

2 answers

5

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 5
Alice, Bob, and Carl each attempt to solve a crossword puzzle. There is a $70 \%$ chance that Alice can solve the puzzle without making a mistake, a $60 \%$ chance that Bob can, and a $85 \%$ chance that Carl can. What is the probability that each one makes a mistake in solving the puzzle? $0.018$ $0.357$ $0.9$ $0.12$

GO Classes asked in Probability Apr 12, 2023

857 views

9 votes

3 answers

6

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? $P(C \mid A, B) \cdot P(A, B)$ $P(C \mid A, B) \cdot P(A) \cdot P(B)$ $P(A \mid B) \cdot P(B \mid C) \cdot P(C)$ $P(A \mid B, C) \cdot P(B \mid C) \cdot P(C)$

GO Classes asked in Probability Apr 12, 2023

621 views

12 votes

4 answers

7

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? $P(E 1, E 2), P(H), P(E 1 \mid H), P(E 2 \mid H)$ $P(E 1, E 2), P(H), P(E 1, E 2 \mid H)$ $P(H), P(E 1 \mid H), P(E 2 \mid H)$ $P(H), P(E 1 \mid H)$

GO Classes asked in Probability Apr 12, 2023

629 views

20 votes

4 answers

8

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 8
Suppose $A$ and $B$ are independent events. Consider the following probabilities. $ \begin{aligned} & P(A, B)=0.15 \\ & P\left(A, B^c\right)=0.45 \\ & P\left(A^c, B\right)=x \\ & P\left(A^c, B^c\right)=y \end{aligned} $ What will be the value of $x+y?$

GO Classes asked in Probability Apr 12, 2023

973 views

8 votes

2 answers

9

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 $P(A \mid B) \geq P(A)$. $P(A \cap B) \geq P(A)+P(B)-1$. $P\left(A \cap B^c\right)=P(A \cup B)-P(B)$.

GO Classes asked in Probability Apr 12, 2023

731 views

12 votes

2 answers

10

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 $\text{ red"}$? $1 / 2$ $3 / 4$ $1 / 6$ $1 / 3$

GO Classes asked in Probability Apr 12, 2023

767 views

14 votes

1 answer

11

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 11
A drug-screening test is used in a group of professional baseball players of whom $4 \%$ actually use illegal drugs. It is found that the test indicates positive in $97 \%$ of those who use drugs and $2 \%$ of those who do ... chosen player in the group with positive test result actually uses drugs? $0.67$ $0.97$ $0.06$ $0.52$

GO Classes asked in Probability Apr 12, 2023

651 views

24 votes

3 answers

12

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 12
Class has $50$ students $20$ male $(M), 25$ brown-eyed $(B)$ For a randomly chosen student, what is the range of possible values for $p=P(M \cup B)?$ $p \leq .4$ $.4 \leq p \leq .5$ $.4 \leq p \leq .9$ $.5 \leq p \leq .9$

GO Classes asked in Probability Apr 12, 2023

784 views

6 votes

3 answers

13

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 13
A box contains three coins: two regular coins and one fake two-headed coin $(P(H)=1),$ You pick a coin at random and toss it. What is the probability that it lands heads up? $1 / 2$ $2 / 3$ $4 / 5$ None of these

GO Classes asked in Probability Apr 12, 2023

638 views

10 votes

4 answers

14

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 14
Consider a three level tree diagram of events happening in a sequence. At first level $A, B$ or $C$ events are possible, at second level $D, E$ or $F$ are possible and at third level $P$ or $Q$ ... third level are $1/2.$ Find $P(A \mid P)?$ $2/3$ $1 / 3$ $1 / 2$ $3 / 4$

GO Classes asked in Probability Apr 12, 2023

792 views

17 votes

1 answer

15

GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 15
For a sample space $\mathrm{S}$ encompassing three events $\mathrm{E}, \mathrm{F},$ and $\mathrm{G},$ if it is given that $P(E)=0.3, P(F)=$ $0.8, P(G)=0.2,$ which of the following can NOT be true ... events Events $\mathrm{E}$ and $\mathrm{F}$ are independent events Events $\mathrm{F}$ and $\mathrm{G}$ are independent events

GO Classes asked in Probability Apr 12, 2023

990 views

To see more, click for the full list of questions or popular tags.

Recent questions tagged goclasses2024_wq8