{"id":24571,"date":"2023-12-06T12:22:56","date_gmt":"2023-12-06T12:22:56","guid":{"rendered":"https:\/\/masterskills.org\/blog\/xac-suat-co-dieu-kien-conditional-probability-la-gi-dac-diem-va-cong-thuc-tinh.html"},"modified":"2023-12-22T09:50:08","modified_gmt":"2023-12-22T02:50:08","slug":"xac-suat-co-dieu-kien-conditional-probability-la-gi-dac-diem-va-cong-thuc-tinh","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/xac-suat-co-dieu-kien-conditional-probability-la-gi-dac-diem-va-cong-thuc-tinh.html","title":{"rendered":"X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n (Conditional Probability) l\u00e0 g\u00ec? \u0110\u1eb7c \u0111i\u1ec3m v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh"},"content":{"rendered":"
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Hi\u0300nh minh ho\u0323a. Ngu\u00f4\u0300n: Digitalvidya.com<\/p>\n<\/figcaption><\/figure>\n

X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n <\/font><\/h2>\n

Kha\u0301i ni\u00ea\u0323m<\/b><\/p>\n

X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n<\/b> trong ti\u00ea\u0301ng Anh la\u0300 Conditional Probability.<\/b><\/p>\n

X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n<\/b> l\u00e0 kh\u1ea3 n\u0103ng, c\u01a1 h\u1ed9i x\u1ea3y ra m\u1ed9t bi\u1ebfn c\u1ed1 ho\u1eb7c k\u1ebft qu\u1ea3 d\u1ef1a tr\u00ean s\u1ed1 l\u1ea7n xu\u1ea5t hi\u1ec7n c\u1ee7a bi\u1ebfn c\u1ed1 ho\u1eb7c k\u1ebft qu\u1ea3 \u0111\u00f3 tr\u01b0\u1edbc \u0111\u00f3.<\/p>\n

X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch nh\u00e2n x\u00e1c su\u1ea5t tr\u01b0\u1edbc \u0111\u00f3 c\u1ee7a bi\u1ebfn c\u1ed1 v\u1edbi x\u00e1c su\u1ea5t c\u1eadp nh\u1eadt c\u1ee7a bi\u1ebfn c\u1ed1. V\u00ed d\u1ee5:<\/p>\n

– Bi\u1ebfn c\u1ed1 A l\u00e0 tr\u1eddi \u0111ang m\u01b0a v\u00e0 x\u00e1c xu\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 A l\u00e0 0,3 hay kh\u1ea3 n\u0103ng h\u00f4m nay tr\u1eddi c\u00f3 m\u01b0a l\u00e0 30%.<\/p>\n

– Bi\u1ebfn c\u1ed1 B l\u00e0 m\u1ed9t s\u1ebd ra kh\u1ecfi nh\u00e0 v\u00e0 x\u00e1c xu\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 B l\u00e0 0,5 hay kh\u1ea3 n\u0103ng h\u00f4m nay ng\u01b0\u1eddi \u0111\u00f3 ra kh\u1ecfi nh\u00e0 l\u00e0 50%.<\/p>\n

X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n s\u1ebd xem x\u00e9t hai bi\u1ebfn c\u1ed1 n\u00e0y v\u1edbi gi\u1ea3 \u0111\u1ecbnh l\u00e0 ch\u00fang c\u00f3 m\u1ed1i quan h\u1ec7 v\u1edbi nhau, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 x\u00e1c su\u1ea5t m\u1ed9t ng\u01b0\u1eddi s\u1ebd ra kh\u1ecfi nh\u00e0 khi tr\u1eddi \u0111ang m\u01b0a.<\/p>\n

\u0110\u1eb7c \u0111i\u1ec3m X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n\u00a0<\/font><\/h3>\n

Gi\u1ea3 s\u1eed c\u00f3 hai bi\u1ebfn c\u1ed1 A v\u00e0 bi\u1ebfn c\u1ed1 B.<\/p>\n

Th\u00f4ng tin bi\u1ebfn c\u1ed1 B ch\u1eafc ch\u1eafn \u0111\u00e3 x\u1ea3y ra s\u1ebd l\u00e0m thay \u0111\u1ed5i x\u00e1c su\u1ea5t x\u1ea3y ra ban \u0111\u1ea7u c\u1ee7a bi\u1ebfn c\u1ed1 A, x\u00e1c su\u1ea5t \u0111\u00e3 \u0111\u01b0\u1ee3c \u0111i\u1ec1u ch\u1ec9nh \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n<\/b> c\u1ee7a A khi \u0111\u00e3 bi\u1ebft B v\u00e0 \u0111\u01b0\u1ee3c k\u00ed hi\u1ec7u l\u00e0 P (A|B).<\/p>\n

C\u00f4ng th\u1ee9c t\u00ednh x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n l\u00e0:<\/i><\/p>\n

P(B|A) = P(A v\u00e0 B) \/ P(A)\u00a0<\/b><\/p>\n

Hay\u00a0<\/i><\/p>\n

P(B|A) = P(A\u2229B) \/ P(A)<\/b><\/p>\n

V\u00ec x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n ph\u1ee5 thu\u1ed9c v\u00e0o c\u00e1c k\u1ebft qu\u1ea3 x\u1ea3y ra tr\u01b0\u1edbc \u0111\u00f3, n\u00f3 c\u0169ng bao h\u00e0m m\u1ed9t s\u1ed1 gi\u1ea3 \u0111\u1ecbnh.<\/p>\n

V\u00ed d\u1ee5 v\u1ec1\u00a0X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n<\/font><\/h3>\n

M\u1ed9t h\u1ecdc sinh l\u1ea5y ng\u1eabu nhi\u00ean m\u1ed9t vi\u00ean bi t\u1eeb m\u1ed9t chi\u1ebfc t\u00fai \u0111\u1ef1ng ba vi\u00ean bi m\u00e0u \u0111\u1ecf, xanh d\u01b0\u01a1ng v\u00e0 xanh l\u1ee5c. M\u1ed7i vi\u00ean bi c\u00f3 c\u01a1 h\u1ed9i \u0111\u01b0\u1ee3c l\u1ea5y nh\u01b0 nhau. H\u1ecfi t\u00ednh x\u00e1c su\u1ea5t l\u1ea5y \u0111\u01b0\u1ee3c vi\u00ean bi xanh l\u1ee5c sau khi l\u1ea5y \u0111\u01b0\u1ee3c vi\u00ean bi \u0111\u1ecf l\u00e0 bao nhi\u00eau?<\/p>\n

Trong l\u1ea7n l\u1ea5y \u0111\u1ea7u, x\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n <\/b>c\u1ee7a vi\u1ec7c c\u1eadu b\u00e9 l\u1ea5y \u0111\u01b0\u1ee3c vi\u00ean bi \u0111\u1ecf l\u00e0 x\u1ea5p x\u1ec9 33% v\u00ec \u0111\u00f3 l\u00e0 m\u1ed9t trong ba k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 x\u1ea3y ra.<\/p>\n

Gi\u1ea3 s\u1eed bi\u1ebfn c\u1ed1 \u0111\u1ea7u ti\u00ean x\u1ea3y ra hay c\u1eadu b\u00e9 \u0111\u00e3 l\u1ea5y ra vi\u00ean bi \u0111\u1ecf, trong t\u00fai ch\u1ec9 c\u00f2n hai vi\u00ean bi m\u00e0u xanh l\u00e1 v\u00e0 xanh d\u01b0\u01a1ng, x\u00e1c su\u1ea5t l\u1ea5y \u0111\u01b0\u1ee3c m\u1ed7i vi\u00ean t\u0103ng l\u00ean 50% do ch\u1ec9 c\u00f2n hai k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 x\u1ea3y ra.<\/p>\n

V\u00ec v\u1eady, x\u00e1c xu\u1ea5t \u0111\u1ec3 l\u1ea5y \u0111\u01b0\u1ee3c vi\u00ean bi m\u00e0u xanh sau khi l\u1ea5y vi\u00ean bi \u0111\u1ecf s\u1ebd l\u00e0 x\u1ea5p x\u1ec9 16,5% hay 33%*50%.<\/p>\n

M\u1ed9t v\u00ed d\u1ee5 kh\u00e1c, x\u00e1c \u0111\u1ecbnh x\u00e1c su\u1ea5t xu\u1ea5t hi\u1ec7n m\u1eb7t s\u1ed1 n\u0103m khi quay m\u1ed9t con x\u00fac x\u1eafc \u0111\u1ed3ng ch\u1ea5t. Do con x\u00fac x\u1eafc c\u00f3 s\u00e1u m\u1eb7t v\u00e0 c\u00e1c k\u1ebft qu\u1ea3 \u0111\u1ec1u c\u00f3 kh\u1ea3 n\u0103ng x\u1ea3y ra nh\u01b0 nhau, c\u00e2u tr\u1ea3 l\u1eddi c\u1ee7a b\u1ea1n l\u00e0 1\/6.<\/p>\n

Gi\u1ea3 s\u1eed c\u00f3 th\u00eam m\u1ed9t th\u00f4ng tin r\u1eb1ng con s\u1ed1 s\u1ebd xu\u1ea5t hi\u1ec7n l\u00e0 s\u1ed1 l\u1ebb. Do ch\u1ec9 c\u00f3 ba s\u1ed1 l\u1ebb l\u00e0 c\u00f3 th\u1ec3 xu\u1ea5t hi\u1ec7n (1,3,5), b\u1ea1n s\u1ebd \u0111i\u1ec1u ch\u1ec9nh l\u1ea1i gi\u00e1 tr\u1ecb \u01b0\u1edbc t\u00ednh c\u1ee7a m\u00ecnh cho x\u00e1c su\u1ea5t s\u1ed1 n\u0103m xu\u1ea5t hi\u1ec7n t\u1eeb 1\/6 l\u00ean 1\/3.<\/p>\n

Ph\u00e2n bi\u1ec7t X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n, X\u00e1c su\u1ea5t k\u1ebft h\u1ee3p v\u00e0 X\u00e1c su\u1ea5t bi\u00ean<\/font><\/h3>\n

– X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n<\/b><\/i> k\u00ed hi\u1ec7u l\u00e0 p(A|B) l\u00e0 x\u00e1c su\u1ea5t x\u1ea3y ra bi\u1ebfn c\u1ed1 A v\u1edbi \u0111i\u1ec1u ki\u1ec7n l\u00e0 bi\u1ebfn c\u1ed1 B \u0111\u00e3 x\u1ea3y ra.<\/p>\n

– X\u00e1c su\u1ea5t bi\u00ean<\/i> hay c\u00f2n g\u1ecdi l\u00e0 x\u00e1c su\u1ea5t v\u00f4 \u0111i\u1ec1u ki\u1ec7n<\/i>, l\u00e0 x\u00e1c su\u1ea5t m\u1ed9t bi\u1ebfn c\u1ed1 x\u1ea3y ra k\u00ed hi\u1ec7u l\u00e0 p(A), kh\u00f4ng b\u1ecb \u1ea3nh h\u01b0\u1edfng b\u1edfi c\u00e1c bi\u1ebfn c\u1ed1 kh\u00e1c hay c\u00e1c th\u00f4ng tin m\u1edbi.<\/p>\n

V\u00ed d\u1ee5 x\u00e1c su\u1ea5t m\u1ed9t c\u1ed5 phi\u1ebfu t\u0103ng l\u00e0 x\u1ea5p x\u1ec9 33% do c\u1ed5 phi\u1ebfu ch\u1ec9 c\u00f3 th\u1ec3 t\u0103ng, gi\u1ea3m ho\u1eb7c gi\u1eef nguy\u00ean gi\u00e1.<\/p>\n

– X\u00e1c su\u1ea5t k\u1ebft h\u1ee3p<\/i> k\u00ed hi\u1ec7u l\u00e0 p(A\u2229B) l\u00e0 x\u00e1c su\u1ea5t c\u1ee7a bi\u1ebfn c\u1ed1 A v\u00e0 bi\u1ebfn c\u1ed1 B c\u00f9ng x\u1ea3y ra. X\u00e1c xu\u1ea5t k\u1ebft h\u1ee3p c\u00f3 th\u1ec3 l\u00e0 x\u00e1c su\u1ea5t giao \u0111i\u1ec3m c\u1ee7a hai ho\u1eb7c nhi\u1ec1u bi\u1ebfn c\u1ed1.<\/p>\n

V\u00ed d\u1ee5 x\u00e1c su\u1ea5t c\u1ed5 phi\u1ebfu c\u1ee7a hai c\u00f4ng ty trong m\u1ed9t danh m\u1ee5c \u0111\u1ea7u t\u01b0 l\u00e0 33% hay (1\/6 +1\/6) = 2\/6 = 1\/3.<\/p>\n

(Theo Investopedia<\/i>)<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n X\u00e1c su\u1ea5t c\u00f3 \u0111i\u1ec1u ki\u1ec7n (ti\u1ebfng Anh: Conditional Probability) l\u00e0 kh\u1ea3 n\u0103ng, c\u01a1 h\u1ed9i x\u1ea3y ra m\u1ed9t bi\u1ebfn c\u1ed1 ho\u1eb7c k\u1ebft qu\u1ea3 d\u1ef1a tr\u00ean s\u1ed1 l\u1ea7n xu\u1ea5t hi\u1ec7n c\u1ee7a bi\u1ebfn c\u1ed1 ho\u1eb7c k\u1ebft qu\u1ea3 \u0111\u00f3 tr\u01b0\u1edbc \u0111\u00f3.\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[414],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/24571"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=24571"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/24571\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=24571"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=24571"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=24571"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}