Untuk setiap kejadian A dan B, berlaku:
P (A
B) = P(A) + P(B) - P(A
B)
- Kejadian A dan B saling lepas jika (A
B) =![begin mathsize 12px style empty set end style](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAALCAYAAABPhbxiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAKIPF7gAAAAJhJREFUeNpjYCAeiAJxLSFFAUB8Boh/AfEHIJ4GxHuB2B6fphyoIlMonwfKfwzEwrg0SQLxNSBmQRID2bIbiDOAeAIujdFAPBvNXxegNBcQv8SlMQ2IpyDxd6P56xcxNtZDMQzgtRHkxxtA7AK1Dd01ffhCtRKI/wOxB5TPB8R5QHwJX6jC/FWLFI/voPEoik+TNBC7EZOMAHsrHuLN9tIOAAAAcXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3R5bGUgbWF0aHNpemU9IjEycHgiPjxtbz4mI3gyMjA1OzwvbW8+PC9tc3R5bGU+PC9tYXRoPuzFJvgAAAAASUVORK5CYII=)
- Kejadian A dan B tidak saling lepas jika (A
B)![begin mathsize 12px style not equal to empty set end style](data:image/png;base64,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)
Diketahui: dua buah dadu dilempar undi sekali.
Ruang sampel dapat ditentukan sebagai berikut.
![](https://core-ruangguru.s3.amazonaws.com/assets/ruang_belajar/questions/q_z8vlxj3439.PNG)
Dari tabel di atas, diperoleh:
n(S) = 36
A = {muncul mata dadu berjumlah 9}
A = {(3 , 6), (4, 5), (5, 4), (6, 3)}
n(A) = 4
B = {muncul mata dadu berjumlah 6}
B = {(1 ,5), (2, 4), (3, 3), (4, 2), (5, 1)}
n(B) = 5
Dari tabel tersebut terlihat bahwa (A
B) =
(kejadian yang saling lepas).
Jadi, peluang muncul mata dadu berjumlah 9 atau 6:
![begin mathsize 12px style P left parenthesis A union B right parenthesis equals P left parenthesis A right parenthesis space plus space P left parenthesis B right parenthesis space minus space P left parenthesis A intersection B right parenthesis P left parenthesis A union B right parenthesis equals fraction numerator n left parenthesis A right parenthesis over denominator n left parenthesis S right parenthesis end fraction plus fraction numerator n left parenthesis B right parenthesis over denominator n left parenthesis S right parenthesis end fraction minus fraction numerator n left parenthesis A intersection B right parenthesis over denominator n left parenthesis S right parenthesis end fraction P left parenthesis A union B right parenthesis equals 4 over 36 plus 5 over 36 plus 0 P left parenthesis A union B right parenthesis equals 9 over 36 end style](data:image/png;base64,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)
Tip!
Banyak ruang-ruang sampel n buah dadu yang dilempar sekali dinyatakan dengan rumus:
n(S) = ![begin mathsize 12px style 6 to the power of n end style](data:image/png;base64,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)
Untuk dua dadu (n = 2) maka:
n(S) =
= 36.
A = {(3 , 6), (4, 5), (5, 4), (6, 3)}
n(A) = 4
B = {(1 ,5), (2, 4), (3, 3), (4, 2), (5, 1)}
n(B) = 5
(A
B) =
(kejadian yang saling lepas)
Peluang muncul mata dadu berjumlah 9 atau 6:
![begin mathsize 12px style P left parenthesis A union B right parenthesis equals P left parenthesis A right parenthesis space plus space P left parenthesis B right parenthesis space P left parenthesis A union B right parenthesis equals fraction numerator n left parenthesis A right parenthesis plus n left parenthesis B right parenthesis over denominator n left parenthesis S right parenthesis end fraction P left parenthesis A union B right parenthesis equals fraction numerator 4 plus 5 over denominator 36 end fraction P left parenthesis A union B right parenthesis equals 9 over 36 end style](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIMAAABwCAYAAAA9m8PRAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAA46CYqAAAABgpJREFUeNrtnUFoVEcYxwcJoUgQipQioRQkiIhIoYcgIUhBSpAcQiFICCIilNJT6cWDFPHgJRQREUGCSBAJiEgOPXgJRUS8SBARkYCIh1KKIB6KhCXwOt/u97aTcd7bNzszb9/O/H/w4b59uy/fzJud+Wbefz6FqM6CtGVhT2b5fhHL7ENd2JS3bt9c/K3k6wW+QWQfpd2VtovP7Zb2Wtqegu/+yuajMeh+3OT3x9iHMU+V57O8vn3z4a9TPdLF5/j1iLRn0r7n45+kXS743n6++J+eGkPuBxV0Utq/0o7zucvsiw98l9fWtyywv071uCntK+X4jbRxfn1P2mzB9x5K+1ba3wW/JNvGoPtBx3v59Sz7UnS9IqujvGW++WgMtv72W4/t1vNROT4o7ZZy/I67Ip0fpS3xa+qGTjo2BtWPUWm/SPtNOf+ZtPceeoUQ5bX1LQvor1M9TrJz29JeSTuvjEdEy/CdfdI2+MKCu6RVx8Ywqf2i7xg+s+WhMYQq71aFBmDTe/Xrr1M9LmgtTcdUOX9Im1aORwpaW0tz3NTSTX5Qi17T/kZZIWwqOlR5twL1DLb+utSjuCrtbMkf07uhhZKK/0777oYS6ORQIPO0gh80DVrUurcPHnqGEOW19S0L6K9TPd6XdqLkj6kByhfSnkv73PC5n5UxNWeRI98JPp7g44UCP2a456Ag7S9pBxyCtDrLGzKAtPHXuR7fK2OhKCj07/x6tcQxmna9NLx/hqPZjP89U+KHOjbOO07f6iyvz2mvi7/B67HXIkwd1LGw02956/TN1V8vvlK3fmOAjeG6qH85+kZDfXPxtwm+AgAAAAAAAECCNFX15FXdBHrTRNVTkV91qcSSJZTqKQvgV10qsaih9Xt6eENPUulx8DnlXCjVUxbAr77VTaAD/Yrogc5t0ZGRfSN26hRCqZ4yz37VpRKLmkmxU1sxJW1dOfaperIR4Nj6VZdKLPqZwop2fKtHY/Cheso8++WkbgIdrmqBla4SCqV6yjz7VZdKzHquXaXQTdlRpauI1rTjUKqnzKNf+ee9qcRS21GVo6uI9ONBqZ5s/MrPe1M3pbajyteik84gF528+ZTajirbIbKJqqcg6qbUdlSBHnPtlHZUZbDiHjO1HVWgx5w2pR1VwGJOqxPbjqpBU2XNZmAahNR2VA0S05TwPDf8bS7/OdFgDUJqO6pCoq/ZXORewFSuxjb+1HZUuWCjQ3jEQ6MJaBCGHFsdwgmOwaYM18K6SgRrNrb6iAmeJS0FWlcBAxxObfURxNc8m5pDY4gHWx2CyhVpp7CuEg+2OoScIzwt/xIBZDzY6BA+8LpCi+OKw8MytQR+qLpmg40vCQWZvdZskGEFAAAAAAAAAAAYbkii50NAC1HukENLwY8r3rjM8TxoMCTufSI6YhQ0hsShJ4NHLW5klcZAD59IBX4a1Ts8kD7xVIUbbbtJJ5f7r2vXBw2mn11YNsMAbRp+gWoe3sYhPDYG2ia4GVslpfJ/YftsDKRZuDmMcUOqmVtCzATyXWFPxJBqEpC5BXRB5hbQnQYhcwtog8wtDcma0pSZAjK3gDbI3AK6IHML6ILMLeVDT0ubautxzkMevpIYlpC5pTPDequ9d4iHwcOp9R6pZ27ZZQiQVwwBLogcWvS6Zhje3nFM9JaHv3lUVdzkcYBJk7DNM549PBVeLomHQCTQzb4kOiuuKpvaGsqYIa4AkaIveC1rU+zRgvUTEBnThht9hINI6jlGOK6YQVXFHS9Qj/BAdJJw6SzylPcfBJAAAAAAAAAAAAAAAIBKkNKbFFsk78OqYsLQzadnDPSsgfSepAL/AdWSJhvcEHJoV9kjVEua0NCgbgso2uMBEoD2fZBOgbQJ9GiadJ8tVEvaASQ9libV0kkB9RJgZjmgBAqpZG5ROSY6m2fGU7vZyNzyv1+5uok2/k6k+MtH5hbQBZlbgHEujcwtCYPMLZFmYel3poDMLaANMreALsjcArqknLkF2VksSSVzC7KzWASZsWduQXYW0AbZWcCOuAHZWUAbZGcBn4DsLKANsrMgXkB2FuI/EjUwMktle6gAAAOGdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdHlsZSBtYXRoc2l6ZT0iMTJweCI+PG1pPlA8L21pPjxtbz4oPC9tbz48bWk+QTwvbWk+PG1vPiYjeDIyMkE7PC9tbz48bWk+QjwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bWk+UDwvbWk+PG1vPig8L21vPjxtaT5BPC9taT48bW8+KTwvbW8+PG1vPiYjeEEwOzwvbW8+PG1vPis8L21vPjxtbz4mI3hBMDs8L21vPjxtaT5QPC9taT48bW8+KDwvbW8+PG1pPkI8L21pPjxtbz4pPC9tbz48bW8+JiN4QTA7PC9tbz48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjxtaT5QPC9taT48bW8+KDwvbW8+PG1pPkE8L21pPjxtbz4mI3gyMjJBOzwvbW8+PG1pPkI8L21pPjxtbz4pPC9tbz48bW8+PTwvbW8+PG1mcmFjPjxtcm93PjxtaT5uPC9taT48bW8+KDwvbW8+PG1pPkE8L21pPjxtbz4pPC9tbz48bW8+KzwvbW8+PG1pPm48L21pPjxtbz4oPC9tbz48bWk+QjwvbWk+PG1vPik8L21vPjwvbXJvdz48bXJvdz48bWk+bjwvbWk+PG1vPig8L21vPjxtaT5TPC9taT48bW8+KTwvbW8+PC9tcm93PjwvbWZyYWM+PG1zcGFjZSBsaW5lYnJlYWs9Im5ld2xpbmUiLz48bWk+UDwvbWk+PG1vPig8L21vPjxtaT5BPC9taT48bW8+JiN4MjIyQTs8L21vPjxtaT5CPC9taT48bW8+KTwvbW8+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bW4+NDwvbW4+PG1vPis8L21vPjxtbj41PC9tbj48L21yb3c+PG1uPjM2PC9tbj48L21mcmFjPjxtc3BhY2UgbGluZWJyZWFrPSJuZXdsaW5lIi8+PG1pPlA8L21pPjxtbz4oPC9tbz48bWk+QTwvbWk+PG1vPiYjeDIyMkE7PC9tbz48bWk+QjwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bWZyYWM+PG1uPjk8L21uPjxtbj4zNjwvbW4+PC9tZnJhYz48L21zdHlsZT48L21hdGg+9YJe5AAAAABJRU5ErkJggg==)