Probability & Permutation — practice questions, page 7
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QuestionA red die and a green die, both fair, are rolled together. What is the probability that the number…QuestionFour letters have been written to four different people and the four addressed envelopes are lying…QuestionA workshop's output comes from two machines: machine P makes 60% of the items and machine Q the…QuestionOne number is picked at random from 1 to 60, every number being equally likely. What is the…QuestionSeven different books are to be stood side by side on a shelf. Two of them, an atlas and a…QuestionA five-member review team is to be chosen from 6 senior staff and 5 junior staff. The team must…QuestionThe five digits 1, 2, 3, 4 and 6 are arranged at random, each used exactly once, to make a…QuestionA pen stand holds 3 blue and 4 red pens. Two pens are taken out together at random and a friend…QuestionA shop's card machine breaks down on any given day with probability 0.1, independently of what…QuestionSix speakers are to address a seminar one after another. Three of them — the chief guest, the…QuestionAn exam paper has three sections, each holding 4 questions. A candidate must attempt exactly 5…QuestionA squad has 10 players, among them a captain and a vice-captain. Four of the ten are picked at…QuestionThe six letters of the word COFFEE are rearranged. In how many of the resulting letter-strings do…QuestionA three-member panel is picked at random from a group of 4 economists, 3 statisticians and 2…QuestionHow many three-digit numbers are there in which all three digits are different and the number…QuestionA student owns 6 different reference books and wants to carry some of them to the reading room,…QuestionTwo events A and B have P(A) = 0.5 and P(B) = 0.3. Let x be the value of P(A or B) when A and B…QuestionFour-letter strings are formed using the letters of the word PRIME, no letter being used more than…QuestionThe letters of the word 'ORANGE' are arranged so that the vowels always come together. How many…QuestionHow many arrangements of the letters of the word 'DAUGHTER' have no two vowels next to each other?QuestionFind the number of arrangements of the letters of the word 'LEADING' in which the vowels do NOT…QuestionThe letters of the word 'OPTICAL' are to be arranged so that the vowels occupy only the even…QuestionArrange the letters of the word 'BALLOON' so that all the vowels come together. How many such…QuestionA team of 6 is to be picked from 12 players so that one particular player is always included and…QuestionThere are 12 points in a plane, of which exactly 5 are collinear. How many distinct straight lines…
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