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Recent questions tagged independent-events
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GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 6
A college has $10$ (non-overlapping) time slots for its courses, and assigns courses to time slots randomly and independently. A student randomly chooses $3$ of the courses to enroll in. What is the probability that there is a conflict in the student's schedule? (answer upto $2$ decimals)
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probability
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14
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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 ...
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20
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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 $x+y?$
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17
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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
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goclasses2024_wq8
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probability
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8
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GATE CSE 2023 | Question: 43
Consider a random experiment where two fair coins are tossed. Let $A$ be the event that denotes $\text{HEAD}$ on both the throws, $B$ be the event that denotes $\text{HEAD}$ on the first throw, and $C$ be the event that denotes $\text{HEAD}$ on the ... . $A$ and $C$ are independent. $B$ and $C$ are independent. $\operatorname{Prob}(B \mid C)=\operatorname{Prob}(B)$
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Feb 15, 2023
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2
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6
DRDO CSE 2022 Paper 1 | Question: 6 (a)
Let $\oplus$ sign denote bitwise addition modulo $2$. Let $n$ and $m$ be integers. Consider the set of $m$ equations on $n$ variables as follows. \[\begin{array}{l} a_{1,1} x_{1} \oplus a_{1,2} x_{2} \oplus \ldots \oplus a_{1, n} x_{n}=b_{ ... $a_{1, n} x_{n}=b_{1}$ if all $x_{i}$'s are picked uniformly and independently at random from $\{0,1\}$.
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Dec 15, 2022
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boolean-algebra
probability
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5
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2
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7
TIFR CSE 2020 | Part A | Question: 7
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
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Feb 10, 2020
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engineering-mathematics
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independent-events
1
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8
ISI2015-MMA-52
Two coins are tossed independently where $P$(head occurs when coin $i$ is tossed) $=p_i, \: i=1,2$. Given that at least one head has occurred, the probability that coins produced different outcomes is $\frac{2p_1p_2}{p_1+p_2-2p_1p_2}$ $\frac{p_1+p_2-2p_1p_2}{p_1+p_2-p_1p_2}$ $\frac{2}{3}$ none of the above
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Sep 23, 2019
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Arjun
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isi2015-mma
probability
independent-events
1
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1
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9
ISI2017-DCG-22
Let $A_1,A_2,A_3, \dots , A_n$ be $n$ independent events such that $P(A_i) = \frac{1}{i+1}$ for $i=1,2,3, \dots , n$. The probability that none of $A_1, A_2, A_3, \dots , A_n$ occurs is $\frac{n}{n+1}$ $\frac{1}{n+1}$ $\frac{n-1}{n+1}$ none of these
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