Question

В пачке 8 тетрадей в линейку и 4 в клетку. Из пачки наугад берут 2 тетради. Какова вероятность того, что обе тетради окажутся в линейку?

Answer 1

Problem Analysis

We have a pack of 8 notebooks in a ruled format and 4 notebooks in a grid format. We need to find the probability of randomly selecting 2 notebooks from the pack and both of them being in the ruled format.

Solution

To find the probability, we need to calculate the ratio of the number of favorable outcomes to the total number of possible outcomes.

Let's calculate the number of favorable outcomes and the total number of possible outcomes.

Favorable Outcomes

To have both notebooks in the ruled format, we need to select 2 notebooks from the 8 ruled notebooks. This can be calculated using the combination formula:

Number of favorable outcomes = C(8, 2)

Using the combination formula, we can calculate the number of ways to choose 2 notebooks from 8 ruled notebooks:

C(8, 2) = 8! / (2! * (8 - 2)!) = 28

Total Possible Outcomes

The total number of possible outcomes is the number of ways to choose any 2 notebooks from the total pack of 12 notebooks. This can also be calculated using the combination formula:

Total possible outcomes = C(12, 2)

Using the combination formula, we can calculate the number of ways to choose 2 notebooks from 12 notebooks:

C(12, 2) = 12! / (2! * (12 - 2)!) = 66

Probability Calculation

Now that we have the number of favorable outcomes and the total number of possible outcomes, we can calculate the probability:

Probability = Number of favorable outcomes / Total possible outcomes

Probability = 28 / 66

Simplifying the fraction, we get:

Probability = 14 / 33

Therefore, the probability of randomly selecting 2 notebooks from the pack and both of them being in the ruled format is 14/33.

Answer

The probability of randomly selecting 2 notebooks from the pack and both of them being in the ruled format is 14/33.