Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

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3721

Probability - Gravner-53.b
Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the number that came up on the die. The player wins if all four Aces are among the ... ) Smith tells you that he recently played this game once and won. That is the probability that he rolled a $6$ on the die?

Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the n...

Pooja Khatri

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Pooja Khatri asked Sep 24, 2018

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3722

Probability - Gravner-53.a
Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the number that came up on the die. The player wins if all four Aces are among the selected cards. (a) Compute the winning probability for this game.

Consider the following game. A player rolls a die. If he rolls $3$ or less, he loses immediately. Otherwise he selects, at random, as many cards from a full deck as the n...

Pooja Khatri

214 views

Pooja Khatri asked Sep 24, 2018

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3723

Probability - Gravner-52.b
Five married couples are seated at random around a round table. (b) Compute the probability that at most one wife does not sit next to her husband.

Five married couples are seated at random around a round table.(b) Compute the probability that at most one wife does not sit next to her husband.

Pooja Khatri

98 views

Pooja Khatri asked Sep 24, 2018

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3724

Probability - Gravner-52.a
Five married couples are seated at random around a round table. (a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent seats).

Five married couples are seated at random around a round table.(a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent s...

Pooja Khatri

171 views

Pooja Khatri asked Sep 24, 2018

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3725

Probability - Gravner-51.b
Ten fair dice are rolled. What is the probability that: (b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.

Ten fair dice are rolled. What is the probability that:(b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.

Pooja Khatri

123 views

Pooja Khatri asked Sep 24, 2018

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1 answer

3726

Probability - Gravner-51.a
Ten fair dice are rolled. What is the probability that: a) At least one $1$ appears.

Ten fair dice are rolled. What is the probability that:a) At least one $1$ appears.

Pooja Khatri

210 views

Pooja Khatri asked Sep 24, 2018

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3727

Probability - Gravner-51.c
Ten fair dice are rolled. What is the probability that: (c) Each of the number $1,2,3$ appears at least once.

Ten fair dice are rolled. What is the probability that:(c) Each of the number $1,2,3$ appears at least once.

Pooja Khatri

169 views

Pooja Khatri asked Sep 24, 2018

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3728

Probability - Gravner-50
Assume that you have an n-element set $U$ and that you select r independent random subsets A1,............Ar $\subset U$. All Ai are chosen so that all 2n choices are equally likely. Compute (in a simple closed form) the probability that the Ai are pairwise disjoint.

Assume that you have an n-element set $U$ and that you select r independent random subsets A1,............Ar $\subset U$. All Ai are chosen so that all 2n choices are equ...

Pooja Khatri

126 views

Pooja Khatri asked Sep 24, 2018

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1 answer

3729

Probability - Gravner-49.c
You have $16$ balls, $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enough to accommodate any number of balls.) (c) What is the probability that each urn contains all three colors?

You have $16$ balls, $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enou...

Pooja Khatri

585 views

Pooja Khatri asked Sep 24, 2018

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3730

Probability - Gravner-49.a
You have $16$ balls, $3$ blue $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enough to accommodate any number of balls.) (a) What is the probability that no urn is empty?

You have $16$ balls, $3$ blue $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are l...

Pooja Khatri

225 views

Pooja Khatri asked Sep 24, 2018

1 votes

0 answers

3731

Probability - Gravner-49.b
You have $16$ balls, $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enough to accommodate any number of balls.) (b) What is the probability that each urn contains $3$ red balls?

You have $16$ balls, $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enou...

Pooja Khatri

289 views

Pooja Khatri asked Sep 24, 2018

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3732

Probability -Gravner- 48
A chocolate egg either contains a toy or is empty. Assume that each egg contains a toy with probability p, independently of other eggs. You have $5$ eggs; open the first one and see if it has a toy inside, then do the same for second one, etc. Let E1 be ... let E2 be the event that you get at least two toys in succession. Compute P(E1) and P(E2) . Are E1 and Ee independent?

A chocolate egg either contains a toy or is empty. Assume that each egg contains a toy with probability p, independently of other eggs. You have $5$ eggs; open the first ...

Pooja Khatri

388 views

Pooja Khatri asked Sep 24, 2018

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3733

Self-doubt
In discrete,can we use X-OR condition if the question uses ''either-or" or it has to be "either-or but not both"?

In discrete,can we use X-OR condition if the question uses ''either-or" or it has to be "either-or but not both"?

Peach

127 views

Peach asked Sep 24, 2018

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1 answer

3734

Rosen-Pigeonhole Principle
An arm wrestler is the champion for a period of 75 hours. (Here, by an hour, we mean a period starting from an exact hour, such as 1 P.M., until the next hour.) The arm wrestler had at least one match an hour, but no more than 125 total matches. Show that there is a period of consecutive hours during which the arm wrestler had exactly 24 matches.

An arm wrestler is the champion for a period of 75 hours. (Here, by an hour, we mean a period starting from an exact hour, such as 1 P.M., until the next hour.) The arm w...

aditi19

1.4k views

aditi19 asked Sep 24, 2018

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3735

Probability -Gravner- 47
An item is defective (independently of other items ) with probability $0.3$ .You have a method of testing whether the item is defective, but it does not always give you correct answer. If the tested item is defective, the method detects the defects with ... tested all of them and the tests detects no defects . What is the probability that none of the $3$ items is defective?

An item is defective (independently of other items ) with probability $0.3$ .You have a method of testing whether the item is defective, but it does not always give you c...

Pooja Khatri

200 views

Pooja Khatri asked Sep 24, 2018

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3736

Probability - Gravner-46
Consider the following game. Pick one card at random from a full deck of $52$ cards. If you pull an Ace, you win outright.If not, then you look at the value of the card($K$,$Q$, and $J$ count as $10$). If the number is $7$ or less you lose ... $9$ the first time, you select $9$ more cards.) If you get at least one Ace, you win. What are your chances of winning this game?

Consider the following game. Pick one card at random from a full deck of $52$ cards. If you pull an Ace, you win outright.If not, then you look at the value of the card($...

Pooja Khatri

217 views

Pooja Khatri asked Sep 24, 2018

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3737

Probability - Gravner-45.b
You roll a die and your score is the number shown on the die. Your friends rolls five dice his score is the number of $6's$ shown. Compute. (b) The probability of event $B$ that your friend's score is strictly larger than yours.

You roll a die and your score is the number shown on the die. Your friends rolls five dice his score is the number of $6's$ shown. Compute.(b) The probability of event $B...

Pooja Khatri

120 views

Pooja Khatri asked Sep 24, 2018

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3738

Probability - Gravner-45.a
You roll a die and your score is the number shown on the die. Your friends rolls five dice his score is the number of $6's$ shown. Compute (a) the probability of even $A$ that the two scores are equal

You roll a die and your score is the number shown on the die. Your friends rolls five dice his score is the number of $6's$ shown. Compute(a) the probability of even $A$ ...

Pooja Khatri

266 views

Pooja Khatri asked Sep 24, 2018

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3739

Limit

sagar27

241 views

sagar27 asked Sep 24, 2018

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3740

Probability - Gravner-44.b
Each day, you independently decide, with probability $p$, to flip a fair coin. Otherwise, you do nothing. (b) What is the probability of getting $10$ Heads before $5$ Tails?

Each day, you independently decide, with probability $p$, to flip a fair coin. Otherwise, you do nothing.(b) What is the probability of getting $10$ Heads before $5$ Tail...

Pooja Khatri

159 views

Pooja Khatri asked Sep 24, 2018

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