Какой будет максимальная сумма при одновременном броске двух игральных костей?

Вероятность также известна как возможность. Это означает математику случая, которая торгует вероятным событием. Значение обозначается от нуля до единицы. В математике было показано, что вероятность угадывает вероятность того, что события произойдут. По сути, вероятность — это масштаб, в котором что-то должно произойти.

Вероятность

Чтобы понять вероятность более правильно, возьмем пример с бросанием игральной кости, возможные исходы – 1, 2, 3, 4, 5 и 6. Вероятность выпадения любого из благоприятных исходов равна 1/6. Поскольку вероятность возникновения любого из событий одинакова, то и шансы получить любое вероятное число одинаковы, в данном случае это либо 1/6, либо 50/3.

Формула вероятности

Probability of an event = {Number of favourable events } ⁄ {number of total events}

P(A) = {Number of ways A occurs} ⁄ {Total number of events}

ИГРАЛЬНАЯ КОСТЬ

Игральные кости — это небольшой блок с от одной до шести меток или точек на ребре, который используется в играх для получения случайной цифры. Кости — это маленькие подбрасываемые блоки с отмеченными сторонами, которые могут останавливаться на несколько цифр. Они используются для создания случайных фигур, часто как часть дополнительных настольных игр, а также игр в кости, настольных игр, ролевых игр и азартных игр.

Обычный кубик представляет собой куб, на каждой из шести граней которого заметно разное количество цифр от одного до шести. При подбрасывании или броске кубик останавливается, и на его большей стороне появляется случайное число от одного до шести, при этом каждое событие равновероятно. Кости также могут иметь вогнутую или неровную форму, а их грани могут быть отмечены цифрами или символами вместо точек. Загруженные кости разыгрываются, чтобы обслуживать одни результаты, а не другие, для побега или развлечения.

Какой будет максимальная сумма при одновременном броске двух игральных костей?

Решение:

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dice.

Two dice are roll at the same time, number of attainable outcome can be 6² = (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when two dice are thrown i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

Maximum total outcome of the two faces of the dice is (6, 6) = 6 + 6 = 12

The probability of obtaining maximum total outcome of the two faces of the dice = 1/36

Похожие проблемы

Вопрос 1: При броске двух игральных костей, какова вероятность того, что на двух гранях игральной кости в сумме выпадет 10?

Решение:

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dies.

Two dice are roll at the same time, number of attainable outcome can be 6²= (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when two dice are thrown i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

The possibility of getting a total of 10 on the two face of the dice will be (5, 5) (6, 4) (4, 6) 

Probability = 3/36

Вопрос 2: При броске трех игральных костей максимальная сумма на трех гранях игральной кости будет равна?

Решение:

Possibility for throwing six sided three dice will be 1, 2, 3, 4, 5 and 6 dots in each (three) dies.

Three dice are roll at the same time, number of attainable outcome can be 6³ = (6 × 6 × 6) = 216 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling three dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of three when three dice are thrown i.e., (1, 1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all three dice are sixes is 18 i.e., (6, 6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when three dice can total 3,

• 3 ways for 4
• 6 ways for 5
• 10 ways for 6
• 15 ways for 7
• 21 ways for 8
• 25 ways for 9
• 27 ways for 10
• 27 ways for 11
• 25 ways for 12
• 21 ways for 13
• 15 ways for 14
• 10 ways for 15
• 6 ways for 16
• 3 ways for 17
• 1 ways for 18

Forming Sums,

As shown above, for three dice the possible sums include every number from three to 18.

Maximum total outcome of the three face die is (6, 6, 6) = 6 + 6 + 6 = 18

Probability = 1/216

Вопрос 3: Когда бросают две кости, какова вероятность того, что в сумме выпадет 5 на двух гранях костей?

Решение:

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dies.

Two dice are roll at the same time, number of attainable outcome can be 6² = (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when we are throwing two dice i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

The possibility of getting a total of 5 on the two face of the dice will be (4, 1), (1, 4), (2, 3), (3, 2). 

Probability = 4/36

Вопрос 4: Когда бросают три игральные кости, какова вероятность того, что в сумме выпадет 17 на трех гранях игральной кости?

Решение:

Possibility for throwing six sided three dice will be 1, 2, 3, 4, 5 and 6 dots in each (three) dies.

Three dice are roll at the same time, number of attainable outcome can be 6³ = (6 × 6 × 6) = 216 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling three dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of three when three dice are thrown i.e., (1, 1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all three dice are sixes is 18 i.e., (6, 6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when three dice can total 3,

• 3 ways for 4
• 6 ways for 5
• 10 ways for 6
• 15 ways for 7
• 21 ways for 8
• 25 ways for 9
• 27 ways for 10
• 27 ways for 11
• 25 ways for 12
• 21 ways for 13
• 15 ways for 14
• 10 ways for 15
• 6 ways for 16
• 3 ways for 17
• 1 ways for 18

Forming Sums,

As shown above, for three dice the possible sums include every number from three to 18

The possibility of getting a total of 17 on the three face of the dice will be (6, 6, 5) (6, 5, 6) (5, 6, 6)

Probability = 3/216

Вопрос 5: Когда бросают две кости, какова вероятность того, что на двух гранях костей выпадет 12 очков?

Решение:

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dies.

Two dice are roll at the same time, number of attainable outcome can be 6²= (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when two dice are thrown i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

There is only one possibility to obtain a total of 12 on the two face of the dice will be (6, 6)

Probability = 1/36