Question

Проводятся две лотереи. В одной из 100 билетов 20 выигрышных, в другой 120 билетов, среди которых 30 выигрышных. Какова вероятность того, что, имея по одному билету каждой из лотерей, получишь хотя бы один выигрыш? Подскажите подробное решение, если не сложно.

Answer 1

Ответ:

Удачи

Пошаговое объяснение:

₁ − билет первой лотереи оказался проигрышным;

₂ − билет второй лотереи оказался проигрышным.

P(A₁)= $\frac{100-20}{100}$=$\frac{80}{100}$=0.8

P(A₂)= $\frac{120-30}{120}$=$\frac{90}{120}$=0.75

Answer 2

Ответ:

Пошаговое объяснение:

смотри фото

Answer 3

Problem Analysis

We are given two lotteries. In the first lottery, there are 100 tickets with 20 winning tickets. In the second lottery, there are 120 tickets with 30 winning tickets. We need to find the probability of winning at least one prize if we have one ticket for each lottery.

Solution

To find the probability of winning at least one prize, we can find the probability of not winning any prize in both lotteries and subtract it from 1.

Let's calculate the probability of not winning any prize in the first lottery. The probability of not winning a prize in the first lottery is given by:

P(not winning in first lottery) = (number of non-winning tickets in first lottery) / (total number of tickets in first lottery)

The number of non-winning tickets in the first lottery is 100 - 20 = 80, and the total number of tickets in the first lottery is 100. Therefore:

P(not winning in first lottery) = 80 / 100 = 0.8

Similarly, let's calculate the probability of not winning any prize in the second lottery. The probability of not winning a prize in the second lottery is given by:

P(not winning in second lottery) = (number of non-winning tickets in second lottery) / (total number of tickets in second lottery)

The number of non-winning tickets in the second lottery is 120 - 30 = 90, and the total number of tickets in the second lottery is 120. Therefore:

P(not winning in second lottery) = 90 / 120 = 0.75

Now, let's calculate the probability of not winning any prize in both lotteries. Since the two lotteries are independent events, we can multiply the probabilities of not winning in each lottery:

P(not winning in both lotteries) = P(not winning in first lottery) * P(not winning in second lottery)

Substituting the values we calculated earlier:

P(not winning in both lotteries) = 0.8 * 0.75 = 0.6

Finally, we can find the probability of winning at least one prize by subtracting the probability of not winning any prize from 1:

P(winning at least one prize) = 1 - P(not winning in both lotteries)

Substituting the value we calculated earlier:

P(winning at least one prize) = 1 - 0.6 = 0.4

Therefore, the probability of winning at least one prize is 0.4.

Answer

The probability of winning at least one prize, given one ticket for each lottery, is 0.4.