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Recent questions tagged probability

3 3 votes
2 2 answers
184
184 views
GO Classes DPP | GATE DA | Probability | Combinatorial Counting or Enumeration
Two fair dice are rolled, one at a time. What is the probability that the second die will show a number higher than showed on the first die?$\frac{5}{12}$ $\frac{7}{12}$ ...
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3 3 votes
2 2 answers
239
239 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
One hundred people line up to board an airplane. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding pass and takes a ra...
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5 5 votes
4 4 answers
390
390 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
There are three doors; behind one is a nice car, and behind each of the other two is a goat eating a bale of straw. You choose a door. Then Monty Hall opens one of the ot...
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7 7 votes
3 3 answers
377
377 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
A multiple choice exam has $4$ choices for each question. The student has studied enough so that the probability they will know the answer to a question is $0.5$, the pro...
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3 3 votes
2 2 answers
260
260 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
Sarah and Bob draw $13$ cards each from a standard deck of $52$ cards. Given that Sarah has exactly two aces, what is the probability that Bob has exactly one ace?$\dfrac...
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3 3 votes
3 3 answers
275
275 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
Consider a clinical test for cancer that can yield either a positive $(+)$ or negative $(-)$ result. Suppose that a patient who truly has cancer has a $1\%$ chance of sli...
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3 3 votes
2 2 answers
271
271 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
Mark all expressions which indicate that $\mathrm{X}$ is independent of $\mathrm{Y}$ given $\mathrm{Z}$.$P(X, Y \mid Z)=P(X \mid Z) P(Y \mid Z) $ $P(X, Y, Z)=P(X, Z) P(Y)...
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3 3 votes
2 2 answers
350
350 views
GO Classes DPP | GATE DA | Probability | Subtraction Principle
Ten tickets numbered $1, 2, 3, \ldots 10.$ Six tickets are selected at random one at a time with replacement. The probability of the largest number appearing on the sele...
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3 3 votes
2 2 answers
284
284 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
Let $\text{E}$ and $\text{F}$ be two independent events, with $\text{P(E) = P(F)}=0.25$. Let $\text{G}$ be another event on the same sample space, which is disjoint from ...
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2 2 votes
3 3 answers
300
300 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
In a probabilistic model, it is given that $\mathrm{P}[A]=\mathrm{a}, \mathrm{P}[B]=\mathrm{b}$, and $\mathrm{P}\left[\left(B^{c} \mid A^{c}\right)\right]=\mathrm{e}$. De...
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0 0 votes
2 2 answers
263
263 views
GO Classes DPP | GATE DA | Probability | Binomial Probability
A biased coin is flipped six times, and the probability of getting a head on a single flip is $0.3$. What is the probability of getting exactly $4$ heads in these $6$ fli...
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3 3 votes
2 2 answers
264
264 views
GO Classes DPP | GATE DA | Probability | Probability using Combinations
A bakery has $ 15 $ different types of pastries, consisting of $ 6 $ fruit pastries and $ 9 $ cream pastries. Assuming that all selections are equally likely, what is the...
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3 3 votes
2 2 answers
271
271 views
GO Classes DPP | GATE DA | Probability | Binomial Probability
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is$\dfrac{1}{6}$  $\dfrac{3}{8}$  $\dfrac{1}{8}$  $\dfrac{1}...
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5 5 votes
2 2 answers
254
254 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
A fair six-sided die is rolled once. If the number obtained is $1,2,$ or $3$, the die is rolled one more time. What is the probability that the total of all numbers obtai...
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2 2 votes
2 2 answers
239
239 views
GO Classes DPP | GATE DA | Probability | Combinatorial Probability
Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $\dfrac{X}{1296}$. The value of $X$ is _______
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2 2 votes
2 2 answers
252
252 views
GO Classes DPP | GATE DA | Probability | Probability based on Combinations
A quality control unit has $12$ machines, out of which exactly $5$ are in good condition. To check whether the unit is operational, the inspectors examine $4$ machines se...
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1 1 vote
2 2 answers
247
247 views
GO Classes DPP | GATE DA | Probability | Expected Value
Each of the nine words in the sentence $\text{"Books open minds and sharpen critical thinking skills daily"}$ is written on a separate piece of paper. These nine pieces o...
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3 3 votes
6 6 answers
443
443 views
GO Classes DPP | GATE DA | Probability | Binomial Probability
For each element in a set of size $2n$, an unbiased coin is tossed. The $2n$ coin tosses are independent. An element is chosen if the corresponding coin toss was a head. ...
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6 6 votes
2 2 answers
321
321 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are$\left(\dfrac{1}{4...
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3 3 votes
4 4 answers
330
330 views
GO Classes DPP | GATE DA | Probability | Complementary Events
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is$\frac{1}{16}$ $\frac{1}{8}$ $\frac{7}{8}$ $\frac{15}{16}$
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5 5 votes
2 2 answers
316
316 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
An unbalanced dice $($with $6$ faces, numbered from $1$ to $6)$ is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is ...
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2 2 votes
2 2 answers
288
288 views
GO Classes DPP | GATE DA | Probability | Conditional Probability
A man visits a couple who have $2$ children. one of the children, a boy, comes into the room. find the probability $P$ that the other is also a boy.$1/3$ $2/3$ $1/2$ $3/4...
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5 5 votes
2 2 answers
499
499 views
GO Classes DPP | GATE CS, DA | Probability | Probability with Counting of Digits
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$ $\left(\dfrac{9}{10}\right)...
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3 3 votes
2 2 answers
395
395 views
GO Classes DPP | GATE CS, DA | Probability | Probability using Counting Techniques
Eight distinct car accidents occurred in a week. Assume that each accident is equally likely to have occurred on any one of the $7$ days of the week, independently of the...
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7 7 votes
3 3 answers
400
400 views
GO Classes DPP | GATE CS, DA | Probability | Independent Events
$E_{1}$ and $E_{2}$ are events in a probability space satisfying the following constraints:$P(E_{1} )$ = $P( E_{2} )$ $P( E_{1}\cup E_{2} )$ = $1$ $E_{1}$ and $E_{2}$ ar...
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4 4 votes
3 3 answers
371
371 views
GO Classes DPP | GATE CS, DA | Probability | Conditional Probability
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next da...
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7 7 votes
3 3 answers
369
369 views
GO Classes DPP | GATE CS, DA | Probability | Conditional Probability
A pair of unbiased dice are rolled together till a sum of either $5$ or $7$ is obtained. What is the probability that $5$ comes before $7$ ? (upto two decimal places)
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2 2 votes
1 1 answer
824
824 views
GATE DA 2026 | Question: 9
Let $M$ be a randomly chosen non-empty subset of $S=\{1,2,3, \ldots, 2026\}$.Which of the following is the probability that the product of all the elements of $M$ is even...
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1 1 vote
1 1 answer
761
761 views
GATE DA 2026 | Question: 10
Suppose that a computer program provides a non-negative and integer-valued random solution to the equation $n_{1}+n_{2}+n_{3}+n_{4}=20$.Which of the following is the prob...
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3 3 votes
3 3 answers
787
787 views
GATE DA 2026 | Question: 18
Suppose a random variable $Z$ follows $\operatorname{Normal}\left(\mu=0, \sigma^{2}=1\right)$ distribution with probability density function $g(z)$ and cumulative distrib...
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