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2 answers
1
1 vote
1 answer
2
If a random coin is tossed $11$ times, then what is the probability that for $7$th toss head appears exactly $4$ times? $5/32$ $15/128$ $35/128$ None of the options
asked Mar 31 in Probability Lakshman Patel RJIT 76 views
1 vote
1 answer
3
If $X, Y$ and $Z$ are three exhaustive and mutually exclusive events related with any experiment and the $P\left(X \right)=0.5P\left(Y \right)$ and $P\left(Z \right)$ = $0.3P\left(Y \right)$. Then $P\left(Y \right)$ = ___________ . $0.54$ $0.66$ $0.33$ $0.44$
asked Mar 31 in Probability Lakshman Patel RJIT 66 views
0 votes
2 answers
4
A box contains $10$ screws, $3$ of which are defective. Two screws are drawn at random with replacement. The probability that none of two screws is defective will be $100\%$ $50\%$ $49\%$ None of these.
asked Mar 31 in Probability Lakshman Patel RJIT 164 views
1 vote
1 answer
5
The probability that top and bottom cards of a randomly shuffled deck are both aces is: $4/52\times 4/52$ $4/52\times 3/52$ $4/52\times 3/51$ $4/52\times 4/51$
asked Mar 30 in Probability Lakshman Patel RJIT 109 views
5 votes
4 answers
6
Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to $3$ decimal places) is ______.
asked Feb 12 in Probability Arjun 1.9k views
0 votes
2 answers
7
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
asked Feb 10 in Probability Lakshman Patel RJIT 225 views
1 vote
2 answers
8
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 of the other winners. ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
asked Feb 10 in Probability Lakshman Patel RJIT 190 views
0 votes
0 answers
9
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it moves to one ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
asked Feb 10 in Probability Lakshman Patel RJIT 85 views
1 vote
2 answers
10
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls drawn? $2.5$ $3$ $3.5$ $4$ None of the above
asked Feb 10 in Probability Lakshman Patel RJIT 175 views
0 votes
1 answer
11
For the distributions given below : Which of the following is correct for the above distributions? Standard deviation of $A$ is significantly lower than standard deviation of $B$ Standard deviation of $A$ is slightly lower than standard deviation of $B$ Standard deviation of $A$ is same as standard deviation of $B$ Standard deviation of $A$ is significantly higher than standard deviation of $B$
asked Jan 13 in Probability Satbir 442 views
1 vote
0 answers
12
So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people's birthdays are uniformly distributed across the $n$ days of the year. (i) How many people must be there in a ... $n=23$, this works out to be 0.53 and Yes it seems to me I am done. Please correct me If I am wrong.
asked Nov 12, 2019 in Probability Ayush Upadhyaya 236 views
1 vote
0 answers
13
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
asked Oct 23, 2019 in Probability ajaysoni1924 192 views
0 votes
1 answer
14
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n-1}$ $\frac{1}{n-2}$
asked Sep 23, 2019 in Probability Arjun 270 views
1 vote
1 answer
15
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
asked Sep 23, 2019 in Probability Arjun 205 views
1 vote
1 answer
16
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
asked Sep 18, 2019 in Probability gatecse 102 views
1 vote
3 answers
17
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability of choosing a non-zero determinant is $\frac{3}{16}$ $\frac{3}{8}$ $\frac{1}{4}$ none of these
asked Sep 18, 2019 in Calculus gatecse 131 views
1 vote
2 answers
18
A basket contains some white and blue marbles. Two marbles are drawn randomly from the basket without replacement. The probability of selecting first a white and then a blue marble is $0.2$. The probability of selecting a white marble in the first draw is $0.5$. What is the probability of ... a blue marble in the second draw, given that the first marble drawn was white? $0.1$ $0.4$ $0.5$ $0.2$
asked Sep 18, 2019 in Probability gatecse 148 views
2 votes
1 answer
19
If $P$ is an integer from $1$ to $50$, what is the probability that $P(P+1)$ is divisible by $4$? $0.25$ $0.50$ $0.48$ none of these
asked Sep 18, 2019 in Probability gatecse 126 views
1 vote
1 answer
20
A die is thrown thrice. If the first throw is a $4$ then the probability of getting $15$ as the sum of three throws is $\frac{1}{108}$ $\frac{1}{6}$ $\frac{1}{18}$ none of these
asked Sep 18, 2019 in Probability gatecse 109 views
2 votes
2 answers
21
Suppose you alternate between throwing a normal six-sided fair die and tossing a fair coin. You start by throwing the die. What is the probability that you will see a $5$ on the die before you see tails on the coin? $\frac{1}{12}$ $\frac{1}{6}$ $\frac{2}{9}$ $\frac{2}{7}$
asked Sep 13, 2019 in Probability gatecse 311 views
0 votes
1 answer
23
Compute the probability that if 10 married couples are seated at random at a round table, then no wife sits next to her husband 1 wife sits next to her husband. pick one of the 10 couples=$\binom{10}{1}$. These couples can interchange their position such that they sit next ... one couple sits together=$\frac{N}{19!}$ so probability that no couple sits together=$1-\frac{N}{19!}$ is this correct?
asked Jun 11, 2019 in Probability aditi19 663 views
4 votes
1 answer
24
Consider the random process: $X\left ( t \right )=U+Vt$ where $U$ is zero-mean Gaussian random variable and $V$ is a random variable uniformly distributed between $0$ and $2.$ Assume $U$ and $V$ statistically independent. The mean value of random process at $t=2$ is ___________
asked Jun 3, 2019 in Probability srestha 289 views
1 vote
0 answers
25
A women's health clinic has four doctors and each patient is assigned to one of them. If a patient givs birth btween 8 am and 4 pm, then her chance of being attended by her assigned doctor is 3/4, otherwise it is 1/4. What is the probability that a patient is attended by the assigned doctor when she gives birth? (A) 25/144 (B) 5/12 (C) 7/12 (D) 1/12
asked May 30, 2019 in Mathematical Logic JAYKISHAN 229 views
1 vote
1 answer
26
If a student copies his assignments from his friend he would get 80 marks. If he had done the assignments independently he would have scored 50 marks out of 100 and if the teacher finds he is cheating he will be penalized and will be given 0 marks. ... he copies 10 such assignments, what is the probability that he will lose more marks with copying than by doing his independent work independently?
asked May 28, 2019 in Probability Asim Siddiqui 4 277 views
0 votes
1 answer
27
In a restaurant each of $n$ customer gives a hat to the hat check person. The hat check person gives the hat back to the customer in a random order. What is expected number of customer who get back their own hat?
asked May 27, 2019 in Probability srestha 182 views
0 votes
1 answer
28
A carnival swing ride swings to the left with probability 0.4 and to the right with probability. If the ride stops after 10 swings, what is the probability that it is exactly at the place it started?
asked May 27, 2019 in Probability Asim Siddiqui 4 186 views
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