Question

Из 10 билетов выигрышными являются 7. Найди вероятность, что из 4 билетов, взятых наугад, 2 билета будут выигрышными. Ответ:​

Answer 1

Ответ:

0,3 проверенно в онлайн мектеп

Answer 2

Problem Statement

We are given that out of 10 tickets, 7 are winning tickets. We need to find the probability that out of 4 randomly chosen tickets, 2 will be winning tickets.

Solution

To find the probability, we need to determine the number of favorable outcomes and the total number of possible outcomes.

The total number of possible outcomes is the number of ways we can choose 4 tickets out of 10, which can be calculated using the combination formula:

Total number of possible outcomes = C(10, 4)

The number of favorable outcomes is the number of ways we can choose 2 winning tickets out of 7 and 2 non-winning tickets out of 3 (since there are only 3 non-winning tickets left after choosing 2 winning tickets). This can also be calculated using the combination formula:

Number of favorable outcomes = C(7, 2) * C(3, 2)

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

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

Let's calculate the probability:

Total number of possible outcomes: Using the combination formula, we have: C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210

Number of favorable outcomes: Using the combination formula, we have: C(7, 2) = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6) / (2 * 1) = 21 C(3, 2) = 3! / (2! * (3-2)!) = 3! / (2! * 1!) = (3 * 2) / (2 * 1) = 3

Number of favorable outcomes = C(7, 2) * C(3, 2) = 21 * 3 = 63

Probability: Probability = Number of favorable outcomes / Total number of possible outcomes = 63 / 210 = 3 / 10 = 0.3

Therefore, the probability that out of 4 randomly chosen tickets, 2 will be winning tickets is 0.3.