# Recent questions tagged sheldon-ross

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If it is assumed that all $\binom{52}{5}$ ... I'm getting answer 0.095 but in the book answer is given 0.0475 where am I going wrong?
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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?
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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?
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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?
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An airline operates a flight having 50 seats. As they expect some passenger to not show up, they overbook the flight by selling 51 tickets. The probability that an individual passenger will not show up is 0.01, independent of all other tourists. Each ticket costs Rs ... not available, the airline has to pay a compensation of Rs.1lakh to that passenger. What is the expected revenue of the airline?
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What are the relevant chapter of probability by sheldon ross to study for gate? I think whole syllabus is within chapter 5,Should i study everything upto chapter 5 or there are some topics that can be skipped.
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Twelve percent of all US households are in California. A total of 3.3 percent of all US households earn over 250000 per year, while a total of 6.3 percent California households earn over 250000 per year. If a randomly chosen US household earns over 250,000 per year, what is the ... 56 * 10^(-3)/(0.033)=0.2291 But the answer given in the instructors manual is .2066 What is wrong with my logic??
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This is an example in the book (A First Course in Probability by Sheldon Ross). A stick of length 1 is split at a point U that is uniformly distributed over (0,1). Determine the expected length of the piece that contains the point 0≤p≤1. So, My doubt here(see the blue mark) is according to proposition g(x) is Lp(U) , what is f(x) why f(x) is not multiplied. in calculating expected value.
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I was reading probability from Sheldon Ross and found below example. A purchaser of electrical components buys them in lots of size 10. It is his policy to inspect 3 components from a lot and to accept the lot if all the 3 are nondefective. If 30 percent of the lots have 4 defective ... part but why they have multiplied it with $\frac{3}{10}$ in the first part and $\frac{7}{10}$ in the second?
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An ordinary deck of 52 playing cards is randomly divided into 4 piles of 13 cards each. Compute the probability that each pile has exactly 1 ace.
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The question in the book is as follows: A football team consist s of 20 offensive and 20 defensive players. The players are to be paired in groups of 2 for the purpose of determining roommates. If the pairing is done at random, what is the probability that there are no offensive- ... \times20 \choose 2,2,...,2$\times 10!$ My questions is: Why is choosing ordered pairs a mistake in this case?
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An urn contains 6 white and 9 black balls. If 4 balls are to be randomly selected without replacement, what is the probability that the first 2 selected are white and the last 2 black. I solved it in this manner : (6C2 * 9C2)/ (15C4) --- getting 36/91 but the answer is (6*5*9*8)/(15*14*13*12) --- 6/91 I cannot understand exactly why my approach is not working over here.
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Balls are randomly removed from an urn that initially contains 20 red and 10 blue balls. (a) What is the probability that all of the red balls are removed before all of the blue ones have been removed? Now suppose that the urn initially contains 20 red, 10 blue, and 8 ... blue, red, green? (d) What is the probability that the group of blue balls is the first of the three groups to be removed?
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From 10 married couples, we want to select group of 6 that is not allowed to contain a married couple. How many choices are there?
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16
Prove $\binom{m+n}{r}$ = $\binom{n}{0}\binom{m}{r}+\binom{n}{1}\binom{m}{r-1}+... +\binom{n}{r}\binom{m}{0}$
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Determine the number of vectors $\{x_{1}...x_{n}\}$, such that each $x_{i}$ is either $0$ or $1$ and $\displaystyle{\sum_{i=1}^{n}x_{i}\geq k}$
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In the below question my query is for (a) part When we are calculating $P\left \{ \frac{-1}{3}< Z< \frac{2}{3} \right \}$ I know that the normal variable X is converted to standard normal variable and then we look for values in normal table but I want to know how the third step came? Please explain anyone.
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A plane is missing and it is presumed that it was equally likely to have gone down in any of three possible regions. Let 1 − αi denote the probability the plane will be found upon a search of the ith region when the plane is, in fact, in that region, i = 1, 2, ... What is the conditional probability that the plane is in the ith region, given that a search of region 1 is unsuccessful, i = 1, 2, 3?
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