151. An unbiased coin is tossed until a head is obtained. What is…

Question Answered step-by-step 151. An unbiased coin is tossed until a head is obtained. What is… 151. An unbiased coin is tossed until a head is obtained. What is the probability that the experiment is finished in (i) 4 or less number of trials, (ii) in 20 or less number of trials?  1.5.2. A balanced die is rolled 3 times. What is the probability of getting: (a) sum greater than 14; Unangemeldet Heruntergeladen am | 08.01.19 04:37 1.5 How to assign probabilities to individual events? | 31 (b) all the face numbers are the same; (c) at least two of the face numbers are the same; (d) getting the sequences 666 or 121 or 112? 1.5.3. An unbiased coin is flipped 3 times. What is the probability of getting (1) exactly one head or (2) at least one head?  1.5.4. A box contains 6 identical chips numbered 1, 2, 3, 4, 5, 6. Two chips are taken one-by-one at random (blind-folded after shuffling well) with replacement. What is the probability that (1) the first number is bigger than the second number? (2) the first number is less than 1 2 of the second number?  1.5.5. What are the probabilities in Exercise 1.5.4 if the sampling is done without replacement? 1.5.6. In Exercise 1.5.4, what is the probability that (1) the number in the second trial is bigger than the number in the first trial and (2) the number in the second trial is bigger than that in the first trial, given that the first trial resulted in the number 1?  1.5.7. A box contains 7 identical marbles except for the color, 4 are red and 3 are green. Two marbles are picked at random one by one without replacement. What is the probability of getting: (a) the sequence RG (red green); (b) exactly one red and one green; (c) RR (red red); (d) exactly 2 red marbles?  1.5.8. In Exercise 1.5.7 suppose a subset of 2 marbles is taken at random or blindfolded by putting the hand in the box and taking 2 together. Answer (a), (b), (c), (d).  1.5.9. Two identical pieces of string of 20 cm are there. One end of each is marked zero and the other end 20. One string is cut at random. Let x be the distance from zero to the point of cut. The second string is cut at random. Let y be the distance from zero to the point of cut. Find the probability that: (i) x < y, (ii) x ≤ y, (iii) x + y ≤ 10, (iv) x + y ≥ 30, (v) 10 ≤ x ≤ 15, (vi) 5 ≤ y ≤ 20, (vii) 5 ≤ x ≤ 10 and 10 ≤ y ≤ 20, (viii) x 2 + y 2 ≤ 10, (ix) x 2 + y 2 = 10. 1.5.10. A floor is paved with identical square tiles of side 10 cm. A circular coin with a diameter of 2 cm is tossed up. What is the probability that: (a) the coin will fall clean; (b) the coin will not fall clean; (c) the coin will cut exactly one of the edges of the tiles?  1.5.11. In Exercise 1.5.10, if the coin is flipped twice, what is the probability that: Unangemeldet Heruntergeladen am | 08.01.19 04:37 32 | 1 Random phenomena (a) on both occasions the coin will fall clean; (b) in exactly one occasion it falls clean; (c) on the first occasion it falls clean and on the second occasion it does not fall clean?  1512. In Exercise 1.5.10, suppose that the sides of the tiles are m units each and the diameter of the coin is d units. What should the connection be between m and d so that the game is fair, which means the probability of the coin falling clean is the same as the probability it does not fall clean (in such a case, in a game of chance, both people betting on each of the two events of falling clean and not falling clean will have the same chance of winning at each trial).  1.5.13. Suppose that the floor is paved with identical rectangular tiles with lengths of 10 cm and a width of 5 cm and a coin with a diameter of 4 cm is tossed. What is the probability that the coin will fall clean?  1.5.14. Suppose that a floor is paved with identical rhombuses of side m units and a circular coin of diameter d is tossed. What is the probability that the coin will fall clean if d is small such that it can fall clean?  1.5.15. In Exercise 1.5.13, if the floor is paved with identical equilateral triangles, then what will be the corresponding probability?  1.5.16. Answer the questions (a) and (b) in Exercise 1.5.10 if the tiles are (1) equilateral triangles with sides of 20 cm each, (2) parallelograms with sides of equal length of 20 cm and (3) hexagons with sides of 20 cm each.  2.2.1. Evaluate the following numbers of permutations, if possible: (1) P(4, 2); (2) P(3, 4); (3) P(−5, 2); (4) P( 1 2 , 2); (5) P( 3 2 , 1 2 ).  2.2.2. If there are 20 students in a class, then their birthdays could be any one of the 365 days 1, 2,... , 365. If no two birthdays are the same or if all students have distinct birthdays, then how many possibilities are there? Unangemeldet Heruntergeladen am | 08.01.19 04:37 2.3 Combinations | 37  223. How many 3-letter words can be made by using the alphabets of the word, (1) mind; (2) big, with (a) no letter is repeated, (b) the letter i is present. 2.2.4. How many 3-digital number plates can be made (1) with no restriction; (2) no numbers should be repeated; (3) one number 5 must be present; (4) the plate should start with a number 5. 2.2.5. In how many ways 10 persons can be seated (a) on the straight line of 4 chairs; (b) on a circular table with 4 chairs? 2.2.6. Evaluate the following Pochhammer symbols: (1) (−5)2 ; (2) (−5)5 ; (3) (−1 2 )3 ; (4) ( 1 3 )4 . 2.2.7. Convert the following number of permutations into Pochhammer notation: (1) P(5, 3); (2) P(10, 2); (3) P(5,0); (4) P(5, 5).  2.2.8. From a box containing 3 red and 5 green identical marbles, three marbles are picked at random (i) with replacement; (ii) without replacement. How many sample points are there in the sample space?  2.2.9. In Exercise 2.2.8, if we are interested in the event of getting exactly 2 red and one green marble, then how many sample points are there favorable to this event? 2.2.10. A coin is tossed 3 times. Write down all possible sequences of head H and tails T.  Math Statistics and Probability SCS 3251 Share QuestionEmailCopy link Comments (0)