Question

Из колоды 36 карт, вытаскивают 5 карт,из колоды 36 карт, вытаскивают 5 карт, найти вероятность того что среди взятых не менее 3 дам или 3 туза

Answer 1

3  всего вариантов  с(36,5)=36!/31!*5! возможно 3 4  дам или 3 4  тузов  тогда всего благоприятных исходов 2* (4*С(32,2)+32)  то есть вероятность 2*(32+4C(32,2))/С(36,5) а там посчитаешь

Answer 2

Calculation of Probability

To find the probability of drawing at least 3 queens or 3 aces from a deck of 36 cards, we need to calculate the total number of favorable outcomes and the total number of possible outcomes.

The total number of possible outcomes is the number of ways we can draw 5 cards from a deck of 36 cards. This can be calculated using the combination formula:

Total number of possible outcomes = C(36, 5)

The total number of favorable outcomes is the number of ways we can draw at least 3 queens or 3 aces from a deck of 36 cards. We can calculate this by considering the following cases:

1. Drawing exactly 3 queens and 2 other cards: We can choose 3 queens from the 4 available queens in C(4, 3) ways, and we can choose 2 other cards from the remaining 32 cards in C(32, 2) ways. 2. Drawing exactly 3 aces and 2 other cards: We can choose 3 aces from the 4 available aces in C(4, 3) ways, and we can choose 2 other cards from the remaining 32 cards in C(32, 2) ways. 3. Drawing 4 queens and 1 other card: We can choose 4 queens from the 4 available queens in C(4, 4) ways, and we can choose 1 other card from the remaining 32 cards in C(32, 1) ways. 4. Drawing 4 aces and 1 other card: We can choose 4 aces from the 4 available aces in C(4, 4) ways, and we can choose 1 other card from the remaining 32 cards in C(32, 1) ways. 5. Drawing all 5 queens or all 5 aces: We can choose all 5 queens or all 5 aces in C(4, 5) ways.

The total number of favorable outcomes is the sum of the outcomes from these cases:

Total number of favorable outcomes = C(4, 3) * C(32, 2) + C(4, 3) * C(32, 2) + C(4, 4) * C(32, 1) + C(4, 4) * C(32, 1) + C(4, 5)

Now we can calculate the probability by dividing the total number of favorable outcomes by the total number of possible outcomes:

Probability = Total number of favorable outcomes / Total number of possible outcomes

Let's calculate the probability using the given formula.