Question

Среди 11 лотерейных билетов 8 выигрышных. На удачу взяли 4 билета. Определить вероятность того, что среди них 3 выигрышных.

Answer 1

3\8=0,375-вероятность того,что 3 билета из 8 окажутся выигрышными

Answer 2

Problem Analysis

We are given that out of 11 lottery tickets, 8 are winning tickets. We also know that 4 tickets are chosen randomly. We need to determine the probability that among these 4 chosen tickets, 3 are winning tickets.

Solution

To solve this problem, we can use the concept of combinations. The number of ways to choose 3 winning tickets out of 8 is given by the combination formula:

C(n, k) = n! / (k! * (n-k)!)

Where n is the total number of winning tickets (8) and k is the number of winning tickets chosen (3).

Similarly, the number of ways to choose 1 losing ticket out of 3 is given by:

C(n, k) = n! / (k! * (n-k)!)

Where n is the total number of losing tickets (3) and k is the number of losing tickets chosen (1).

The total number of ways to choose 4 tickets out of 11 is given by:

C(n, k) = n! / (k! * (n-k)!)

Where n is the total number of tickets (11) and k is the number of tickets chosen (4).

To find the probability, we divide the number of favorable outcomes (choosing 3 winning tickets and 1 losing ticket) by the total number of possible outcomes (choosing any 4 tickets).

Let's calculate the probability.

Calculation

The number of ways to choose 3 winning tickets out of 8 is:

C(8, 3) = 8! / (3! * (8-3)!) = 56

The number of ways to choose 1 losing ticket out of 3 is:

C(3, 1) = 3! / (1! * (3-1)!) = 3

The total number of ways to choose 4 tickets out of 11 is:

C(11, 4) = 11! / (4! * (11-4)!) = 330

Therefore, the probability of choosing 3 winning tickets and 1 losing ticket out of 4 is:

P = (number of favorable outcomes) / (total number of possible outcomes) = (56 * 3) / 330 = 168 / 330

Simplifying the fraction, we get:

P = 0.5091

So, the probability of choosing 3 winning tickets and 1 losing ticket out of 4 is approximately 0.5091.

Answer

The probability of choosing 3 winning tickets and 1 losing ticket out of 4 is approximately 0.5091.