By Birger Iversen
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Additional resources for Ecole D'Ete de Probabilites: Processus Stochastiques
Here S consists of all the points on the bottom of the box. Let the rectangular area on the right represent these points. Let A and B be the events that the pencil drops into the corresponding areas illustrated on the right. e. which is uncountable. Remark: If the sample space S is finite or countably infinite, then every subset of S is an event. 4, then for technical reasons (which lie beyond the scope of this text) some subsets of S cannot be events. However, in all cases the events shall form a a-algebra & of subsets of S.
Iij There are 4 kings among the 52 cards; hence p = 4 1 = B. Only the first case is not favorable to the given event; 7 hence p = 5. (iv) There are 4 + 3 + 5 = 12 marbles, of which 4 are white; hence p = = $. CHAP. 10. Two cards are drawn a t random from an ordinary deck of 52 cards. Find the probability p that (i) both are spades, (ii) one is a spade and one is a heart. There are (",") = 1326 ways to draw 2 cards from 52 cards. 11. Three light bulbs are chosen a t random from 15 bulbs of which 5 are defective.
50. 54. 59. 48 = 624, (iii) 10 045 - 40 = 10,200. 60. (i) (:)(:) (ii) ( (:)(:) 21 5 3)(2) (iii) 19 (iv) 19 - 5 ! = 1,596,000 (v) 19. 5! = 228,000 (vi) 4 (:)* (i). (E) ("2") (y) * 3 ! = 1140 5! = 91,200 Ei! = 22,800 (vii) 4 4! = 4560 (viii) 18,240 (same a:3 (vii)) 4! = 18,240 (ix) 4 . (y) - 3 ' = 4560 (x) 4 * 1 9 * 5 ! 61. 9! 62. 1680/3! 63. 3! - 1680 or 10! 3! 2! 64. 12! 3! 65. - 12! 3! 66. 2n-1 - 1 2*67' 14 ! 2! 4! 69. 2 2 3 4 4 The eighteen elements of the product set are listed to the right of the tree diagram.
Ecole D'Ete de Probabilites: Processus Stochastiques by Birger Iversen