Question

Монету подбрасывают несколько раз так,что каждый раз с равной вероятностью выпадает «орел» или «решка».Найдите вероятность того,что при первых трех подбрасываниях и «орел» и «решка» выпадут хотя бы по одному разу.

Answer 1

Монету подбрасывают 3 раза. 

Возможные комбинации:

ООО

РРР

ООР

ОРР

РОО

РРО

ОРО

РОР

8 - общее число возможных событий.

6 - в стольких случаях в комбинации выпадает и орел, и решка. 

Делим благоприятные = 6 на все возможные = 8,  6/8=0.75 

 

Answer 2

Probability of Getting at Least One Head and One Tail in Three Tosses

When tossing a coin multiple times with an equal probability of getting "heads" or "tails" each time, the probability of getting at least one head and one tail in the first three tosses can be calculated.

The probability of the complementary event (i.e., the probability of not getting at least one head and one tail in three tosses) can be calculated first. Then, the probability of the desired event can be found by subtracting the probability of the complementary event from 1.

The probability of the complementary event can be calculated using the formula: P(complementary event) = 1 - P(getting all heads) - P(getting all tails) where P(getting all heads) and P(getting all tails) can be calculated using the binomial distribution formula.

The binomial distribution formula is given by: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k) where: - n is the number of trials - k is the number of successful trials - p is the probability of success on each trial - C(n, k) is the number of combinations of n items taken k at a time

Let's calculate the probability step by step.

Calculating the Probability of the Complementary Event

The probability of getting all heads or all tails in three tosses can be calculated using the binomial distribution formula.

For getting all heads: P(getting all heads) = C(3, 3) * (1/2)^3 For getting all tails: P(getting all tails) = C(3, 3) * (1/2)^3

Let's calculate these probabilities.

Calculating the Probability of the Desired Event

After calculating the probabilities of getting all heads and all tails, we can find the probability of the complementary event and then the probability of the desired event.

Let's proceed with the calculations.