Формула вероятности подбрасывания монеты

Вероятность — это раздел математики. Вероятность показывает, насколько вероятно событие. Одним словом, это можно назвать возможностью, т. е. возможностью наступления события. Его значение всегда лежит в диапазоне от 0 (ноль) до 1 (единица). 0 указывает на невозможное событие, а 1 указывает на определенное событие. Формула вероятности события приведена ниже,

Вероятность события P(Event)=(Количество благоприятных исходов)/(Общее количество возможных исходов)

Вероятность подбрасывания монеты

Прежде чем перейти к концепции, сначала давайте разберемся с возможными исходами при подбрасывании монеты. При подбрасывании монеты возможны только 2 исхода. Это Голова и Хвост. Итак, согласно приведенной выше формуле вероятности, формула вероятности подбрасывания монеты задается как

Coin Toss Probability Formula = (Number of favorable outcomes)/ (Total number of possible outcomes)

Here, when a single coin is tossed – Total number of possible outcomes = 2

So, simplify above formula for single coin toss as,

Coin Toss Probability Formula for single coin toss = (Number of favorable outcomes)/2

Примеры проблем

Вопрос 1: Какова вероятность того, что выпадет решка при подбрасывании одной монеты.

Решение:

Let A be the event of getting head when a coin is tossed.

Number of favorable outcomes – {Head} = 1

As per the coin toss probability formula when a single coin is tossed, the probability of getting head P(A) = Number of favorable outcomes/2

P(A) = 1/2 = 0.5

So there is a 50% chance of getting head when a coin is tossed.

Вопрос 2: Какова вероятность того, что при подбрасывании двух монет выпадет хотя бы 1 решка.

Решение:

Let B be the event of getting at least 1 tail when two coins are tossed.

Number of favorable outcomes – {(Head, Tail), (Tail, Head), (Tail, Tail)} = 3

Total possible outcomes – {(Head, Tail), (Tail, Head), (Tail, Tail), (Head, Head)} = 4

As per the coin toss probability formula, Probability of getting atleast 1 tail when 2 coins are tossed P(B) = Number of favorable outcomes/Total number of possible outcomes

P(B) = 3/4 = 0.75

So there are 75% of chances of getting at least 1 tail when two coins are tossed.

Вопрос 3: Какова вероятность выпадения орла или решки при подбрасывании двух монет.

Решение:

Let C be the event of getting head or tail when a coin is tossed.

Number of favorable outcomes – {Head, Tail} = 2

As per the coin toss probability formula when a single coin is tossed, the probability of getting head or tail P(C) = Number of favorable outcomes/2

P(C) = 2/2 = 1

So there is a 100% chance of getting head or tail when a single coin is tossed.

This is an example for sure (or) certain event.

Вопрос 4: Какова вероятность одновременного выпадения орла и решки при подбрасывании одной монеты.

Решение:

Let D be the event of getting head and tail when a coin is tossed.

Here there are no favorable outcomes because when a coin is tossed only 1 possible outcome is obtained either a head or tail but both are not obtained.

Number of favorable outcomes – {} = 0

As per the coin toss probability formula when a single coin is tossed, Probability of getting head and tail P(D)= Number of favorable outcomes/2

P(D) = 0/2 = 0

So there are 0% chances of getting head and tail at the same time when a coin is tossed. 

This is an example of an impossible event.

Вопрос 5: Какова вероятность выпадения всех трех решек при одновременном подбрасывании трех монет.

Решение:

Let E be the event of getting  all three heads when 3 coins are tossed.

When 3 coins are tossed the possible outcomes are ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})

So total number of possible outcomes = 8

The total possible outcomes can also be found by multiplying the number of outcomes of each event together. Here 3 coins are tossed. For each coin toss, there will 2 outcomes. So by multiplying outcomes of each toss i.e., 2 × 2 × 2 = 8 total number of possible outcomes are obtained.

Number of favorable outcomes – {HHH} = 1

As per the coin toss probability formula, Probability of getting all three heads 

P(E) = Number of favorable outcomes/Total number of possible outcomes

P(E) = 1/8 = 0.125

So, there is 12.5% chances of getting all 3 heads when 3 coins are tossed.

Вопрос 6: Какова вероятность того, что при одновременном подбрасывании 3 монет выпадет не менее двух орлов.

Решение:

Let F be the event of getting atleast two heads when 3 coins are tossed.

When 3 coins are tossed the possible outcomes are ({HHH}, {HHT}, {HTH}, {THH}, {HTT}, {TTH}, {THT}, {TTT})

So, the total number of possible outcomes = 8

Number of favorable outcomes – ({HHT}, {HTH}, {THH}, {HHH}) = 4

As per the coin toss probability formula, the Probability of getting at least two heads

P(F)= Number of favorable outcomes/Total number of possible outcomes

P(F) = 4/8 = 1/2 = 0.5

So, there is 50% chance of getting atleast two heads when 3 coins are tossed.