Tr\u01b0\u1edbc h\u1ebft ta x\u00e9t m\u1ed9t v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n, gi\u1ea3 s\u1eed c\u00f3 hai ng\u01b0\u1eddi l\u00e0 A v\u00e0 B c\u00f9ng ch\u01a1i tr\u00f2 \u0111\u00e1nh b\u1ea1c ho\u00e0n to\u00e0n may r\u1ee7i (\u00fd n\u00f3i kh\u00f4ng ch\u01a1i gian). M\u1ed7i l\u1ea7n ch\u01a1i 1 \u0111\u1ed3ng. C\u01a1 h\u1ed9i \u0111\u1ec3 A ho\u1eb7c B th\u1eafng 1 \u0111\u1ed3ng hay thua 1 \u0111\u1ed3ng l\u00e0 nh\u01b0 nhau, v\u00e0 \u0111\u1ec1u b\u1eb1ng 1\/2. Gi\u1ea3 s\u1eed l\u00fac b\u1eaft \u0111\u1ea7u ch\u01a1i, A v\u00e0 B \u0111\u1ec1u c\u00f3 s\u1eb5n s\u1ed1 ti\u1ec1n l\u00e0 a v\u00e0 b t\u01b0\u01a1ng \u1ee9ng. Tr\u00f2 ch\u01a1i \u0111\u01b0\u1ee3c ti\u1ebfn h\u00e0nh \u0111\u1ebfn khi c\u00f3 m\u1ed9t b\u00ean thua s\u1ea1ch th\u00ec ng\u1eebng. H\u1ecfi \u0111\u1ebfn l\u00fac ng\u1eebng ch\u01a1i, kh\u1ea3 n\u0103ng \u0111\u1ec3 A s\u1ea1ch t\u00fai l\u00e0 bao nhi\u00eau?<\/p>\n\n\n\n
Ta th\u1eed t\u00ednh sau m\u1ed9t l\u1ea7n ch\u01a1i b\u1ea1c trung b\u00ecnh c\u00e1c k\u1ebft qu\u1ea3 m\u00e0 A ch\u1edd \u0111\u1ee3i l\u00e0 bao nhi\u00eau? Sau m\u1ed9t l\u1ea7n ch\u01a1i, kh\u1ea3 n\u0103ng \u0111\u1ec3 A c\u00f3 ho\u1eb7c a +1 \u0111 ho\u1eb7c a – 1 \u0111 l\u00e0 nh\u01b0 nhau v\u00e0 b\u1eb1ng 1\/2, v\u00ec v\u1eady b\u00ecnh qu\u00e2n sau m\u1ed9t l\u1ea7n ch\u01a1i A c\u00f3 th\u1ec3 v\u1eabn c\u00f3 a \u0111\u1ed3ng. Qua hai l\u1ea7n ch\u01a1i, t\u00ecnh hu\u1ed1ng \u0111\u01b0\u1ee3c thua b\u1ea1c c\u1ee7a A c\u00f3 th\u1ec3 c\u00f3 b\u1ed1n lo\u1ea1i. (\u0111\u01b0\u1ee3c, \u0111\u01b0\u1ee3c) (\u0111\u01b0\u1ee3c, thua) (thua, \u0111\u01b0\u1ee3c) (thua, thua).<\/p>\n\n\n\n
C\u1ea3 b\u1ed1n t\u00ecnh hu\u1ed1ng \u0111\u1ec1u c\u00f3 kh\u1ea3 n\u0103ng ngang nhau. V\u00ec v\u1eady sau hai l\u1ea7n ch\u01a1i s\u1ed1 ti\u1ec1n c\u1ee7a A c\u00f3 th\u1ec3 l\u00e0 a +2 \u0111 ho\u1eb7c a – 2 \u0111 (c\u1ea3 hai l\u1ea7n \u0111\u1ec1u \u0111\u01b0\u1ee3c ho\u1eb7c c\u1ea3 hai l\u1ea7n \u0111\u1ec1u thua) \u0111\u1ec1u c\u00f3 kh\u1ea3 n\u0103ng b\u1eb1ng , c\u00f2n kh\u1ea3 n\u0103ng A c\u00f3 a \u0111\u1ed3ng (m\u1ed9t \u0111\u01b0\u1ee3c, m\u1ed9t thua ho\u1eb7c m\u1ed9t thua, m\u1ed9t \u0111\u01b0\u1ee3c) c\u00f3 kh\u1ea3 n\u0103ng b\u1eb1ng . V\u00ec v\u1eady s\u1ed1 ti\u1ec1n b\u00ecnh qu\u00e2n A c\u00f3 th\u1ec3 c\u00f3 l\u00e0: (a +2)1\/4 + a x 1\/2 + (a – 2)1\/4 = a \u0111\u1ed3ng<\/p>\n\n\n\n
Qua c\u00e1ch t\u00ednh to\u00e1n t\u01b0\u01a1ng t\u1ef1 ta c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y d\u00f9 qua bao nhi\u1ec1u l\u1ea7n ch\u01a1i, s\u1ed1 ti\u1ec1n b\u00ecnh qu\u00e2n m\u00e0 A nh\u1eadn \u0111\u01b0\u1ee3c v\u1eabn l\u00e0 a \u0111\u1ed3ng.<\/p>\n\n\n\n
C\u0169ng l\u00ed lu\u1eadn t\u01b0\u01a1ng t\u1ef1, B c\u0169ng s\u1ebd c\u00f3 b \u0111\u1ed3ng sau m\u1ed9t s\u1ed1 l\u1ea7n ch\u01a1i. K\u1ebft th\u00fac cu\u1ed9c \u0111\u00e1nh b\u1ea1c v\u1edbi A c\u00f3 th\u1ec3 c\u00f3 hai lo\u1ea1i k\u1ebft c\u1ee5c: c\u00f3 0 \u0111 t\u1ee9c<\/p>\n\n\n\n
A b\u1ecb thua s\u1ea1ch t\u00fai ho\u1eb7c a +b \u0111\u1ed3ng khi B b\u1ecb thua s\u1ea1ch t\u00fai. Gi\u1ea3 s\u1eed kh\u1ea3 n\u0103ng \u0111\u1ec3 A thua s\u1ea1ch l\u00e0 x, kh\u1ea3 n\u0103ng \u0111\u1ec3 B thua s\u1ea1ch t\u00fai l\u00e0 1 – x. Th\u1ebf nh\u01b0ng k\u1ebft qu\u1ea3 trung b\u00ecnh m\u00e0 A ch\u1edd \u0111\u1ee3i l\u1ea1i l\u00e0 a \u0111\u1ed3ng n\u00ean 0 x x + (a + b) x (1- x) = a.<\/p>\n\n\n\n
T\u1eeb \u0111\u00f3 ta c\u00f3: x = b\/ a+b. T\u1ee9c kh\u1ea3 n\u0103ng \u0111\u1ec3 A thua s\u1ea1ch t\u00fai l\u00e0 b\/ a+b. T\u01b0\u01a1ng t\u1ef1 kh\u1ea3 n\u0103ng \u0111\u1ec3 b thua s\u1ea1ch t\u00fai l\u00e0 a\/ a+b. T\u1ee9c kh\u1ea3 n\u0103ng \u0111\u1ec3 hai ng\u01b0\u1eddi thua s\u1ea1ch t\u00fai l\u00e0 t\u1ec9 l\u1ec7 ng\u01b0\u1ee3c v\u1edbi s\u1ed1 ti\u1ec1n h\u1ecd c\u00f3 ban \u0111\u1ea7u.<\/p>\n\n\n\n
Ta l\u1ea1i quay v\u1ec1 vi\u1ec7c tr\u00fang qu\u1ea3 trong th\u1ecb tr\u01b0\u1eddng ch\u1ee9ng kho\u00e1n. Th\u1ecb tr\u01b0\u1eddng ch\u1ee9ng kho\u00e1n ch\u00ednh l\u00e0 m\u1ed9t s\u00f2ng b\u1ea1c kh\u00f4ng c\u00f3 ch\u01a1i gian (s\u00f2ng b\u1ea1c c\u00f4ng b\u1eb1ng) trong \u0111\u00f3 c\u00f3 c\u1ea3 c\u01a1 may l\u1eabn r\u1ee7i ro. V\u1edbi m\u1ed7i ng\u01b0\u1eddi \u0111\u1ea7u t\u01b0 th\u00ec c\u01a1 may v\u00e0 r\u1ee7i ro l\u00e0 nh\u01b0 nhau. M\u1ed9t ng\u01b0\u1eddi tham gia mua \u0111\u1ea7u phi\u1ebfu l\u00e0 tham gia m\u1ed9t cu\u1ed9c \u0111\u00e1nh b\u1ea1c c\u00f4ng b\u1eb1ng. C\u00e1c \u0111\u1ea5u th\u1ee7 c\u00f3 th\u1ec3 c\u00f3 c\u00e1ch \u0111\u1ea7u t\u01b0 gi\u1ed1ng c\u00e1c \u0111\u1ea5u th\u1ee7 kh\u00e1c, nh\u01b0ng c\u0169ng c\u00f3 nh\u1eefng ng\u01b0\u1eddi c\u00f3 vai v\u1ebf: \u0111\u1ea7u t\u01b0 v\u1ed1n v\u00e0o c\u01a1 c\u1ea5u qu\u1ea3n l\u00ed \u0111\u00f2i h\u1ecfi v\u1ed1n \u0111\u1ea7u t\u01b0 l\u1edbn, c\u00f3 kh\u1ea3 n\u0103ng v\u01b0\u1ee3t xa nh\u1eefng \u0111\u1ed1i t\u01b0\u1ee3ng kh\u00e1c. V\u00ec v\u1eady trong cu\u1ed9c ch\u01a1i b\u1ea1c \u201cc\u00f4ng b\u1eb1ng\u201d n\u00e0y kh\u1ea3 n\u0103ng thua s\u1ea1ch t\u00fai c\u1ee7a \u00f4ng ta \u00edt h\u01a1n c\u00e1c \u0111\u1ea5u th\u1ee7 kh\u00e1c nhi\u1ec1u, n\u00f3i c\u00e1ch kh\u00e1c ng\u01b0\u1eddi n\u00e0y c\u00f3 \u0111\u1ea3m b\u1ea3o \u0111\u1ec3 r\u1ee7i ro th\u1ea5p h\u01a1n c\u00e1c \u0111\u1ed1i th\u1ee7 b\u00ecnh th\u01b0\u1eddng kh\u00e1c.<\/p>\n\n\n\n
T\u1eeb g\u00f3c \u0111\u1ed9 \u0111\u00f3 c\u00f3 th\u1ec3 n\u00f3i \u0111\u1ea7u t\u01b0 mua v\u1ed1n c\u00f3 \u01b0u th\u1ebf h\u01a1n mua \u0111\u1ea7u phi\u1ebfu.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: V\u1ec1 tr\u00f2 \u0111\u00e1nh b\u1ea1c.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Tr\u01b0\u1edbc h\u1ebft ta x\u00e9t m\u1ed9t v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n, gi\u1ea3 s\u1eed c\u00f3 hai ng\u01b0\u1eddi l\u00e0 A v\u00e0 B c\u00f9ng ch\u01a1i tr\u00f2 \u0111\u00e1nh b\u1ea1c ho\u00e0n to\u00e0n may r\u1ee7i (\u00fd n\u00f3i kh\u00f4ng ch\u01a1i gian). M\u1ed7i l\u1ea7n ch\u01a1i 1 \u0111\u1ed3ng. C\u01a1 h\u1ed9i \u0111\u1ec3 A ho\u1eb7c B th\u1eafng 1 \u0111\u1ed3ng hay thua 1 \u0111\u1ed3ng l\u00e0 nh\u01b0 nhau, v\u00e0 \u0111\u1ec1u […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[15,9],"tags":[],"class_list":["post-7638","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7638","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=7638"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7638\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}