Question

Два дилера имеют по 3 пакета акций. Вероятность продажи каждого пакета акций равны соответственно 0,7 - для первого дилера и 0,8 - для второго. Найти вероятность того, что у обоих будет одинаковое количество продаж.

Answer 1

Решение
Пусть события: Ai, Bi – вероятность продажи  соответственно 
1-м и  2-м дилером при i -й продаже (i =1,2);
Событие С произойдет, если  у обоих будет одинаковое количество продаж
Итак
Используя теоремы сложения для несовместных и умножения для независимых событий, получим:
решение во вкладыше

Answer 2

Probability of Selling Stocks

To find the probability that both dealers will have the same number of stock sales, we can use the binomial distribution formula. The probability of selling a stock for the first dealer is 0.7, and for the second dealer, it is 0.8.

The probability mass function of the binomial distribution is given by: P(X = k) = (n choose 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

Calculation

Let's calculate the probability that both dealers will have the same number of stock sales.

For the first dealer (p = 0.7): - Probability of selling 0 stocks: P(X = 0) = (3 choose 0) * 0.7^0 * (1 - 0.7)^(3 - 0) - Probability of selling 1 stock: P(X = 1) = (3 choose 1) * 0.7^1 * (1 - 0.7)^(3 - 1) - Probability of selling 2 stocks: P(X = 2) = (3 choose 2) * 0.7^2 * (1 - 0.7)^(3 - 2) - Probability of selling 3 stocks: P(X = 3) = (3 choose 3) * 0.7^3 * (1 - 0.7)^(3 - 3)

For the second dealer (p = 0.8): - Probability of selling 0 stocks: P(X = 0) = (3 choose 0) * 0.8^0 * (1 - 0.8)^(3 - 0) - Probability of selling 1 stock: P(X = 1) = (3 choose 1) * 0.8^1 * (1 - 0.8)^(3 - 1) - Probability of selling 2 stocks: P(X = 2) = (3 choose 2) * 0.8^2 * (1 - 0.8)^(3 - 2) - Probability of selling 3 stocks: P(X = 3) = (3 choose 3) * 0.8^3 * (1 - 0.8)^(3 - 3)

Result

After calculating the probabilities for both dealers, we can sum the probabilities of having the same number of stock sales for each possible outcome (0, 1, 2, or 3 sales) and find the total probability.

Let's proceed with the calculations.