Question

В пачке лежат 10000 билетов с номерами от 0000 до 9999. Назовем билет интересным, если разность каких-либо двух соседних цифр его номера равна 5. Найдите вероятность того, что взятый наудачу билет из пачки окажется интересным

Answer 1

Для того, чтобы билет был интересным, нужно, чтобы в его номере присутствовали числа
05, 16, 27, 38, 49, 50, 61, 72, 83, 94
Всего 10 пар.
Пусть ab - одно из этих чисел. Тогда номер интересного билета может выглядеть так:
ab**
*ab*
**ab
где вместо звёздочек стоят цифры от 0 до 9. То есть для каждой пары чисел есть 3 возможных варианта расположения в номере билета, причём при каждом варианте расположения будет 100 различных номеров билетов.
Таким образом, всего интересных билетов будет 10*3*100 = 3000 штук.
Тогда вероятность вытянуть такой билет составит $P={3000}/{10000}=0,3$

Answer 2

Probability of selecting an interesting ticket

To find the probability of selecting an interesting ticket from a pack of 10,000 tickets with numbers ranging from 0000 to 9999, we need to determine the number of interesting tickets and divide it by the total number of tickets.

An interesting ticket is defined as a ticket where the difference between any two adjacent digits in its number is equal to 5.

Let's break down the problem into smaller steps:

Step 1: Determine the number of interesting tickets To find the number of interesting tickets, we can analyze the possible combinations of adjacent digits that satisfy the condition.

There are four positions in the ticket number: thousands, hundreds, tens, and units. For each position, there are nine possible adjacent digit pairs that have a difference of 5:

- (0, 5) - (1, 6) - (2, 7) - (3, 8) - (4, 9) - (5, 0) - (6, 1) - (7, 2) - (8, 3) - (9, 4)

For the thousands position, there are nine possible pairs, and for the hundreds, tens, and units positions, there are eight possible pairs each.

Therefore, the total number of interesting tickets can be calculated as follows:

Number of interesting tickets = 9 * 8 * 8 * 8 = 4608

Step 2: Determine the total number of tickets The total number of tickets in the pack is given as 10,000.

Step 3: Calculate the probability The probability of selecting an interesting ticket can be calculated by dividing the number of interesting tickets by the total number of tickets:

Probability = Number of interesting tickets / Total number of tickets Probability = 4608 / 10000 Probability ≈ 0.4608

Therefore, the probability of randomly selecting an interesting ticket from the pack is approximately 0.4608.

Please note that the above calculation assumes that all tickets in the pack are equally likely to be selected and that the selection process is random.