Question

У туристов были 3 банки с мясом, 2 банки с овощами и 2 – с фруктами. Во время дождя надписи на банках были стерты. Туристам надо открыть 3 банки. Какова вероятность того, что банки будут отличаться содержимым?

Answer 1

3/7 * 2/7 * 2/7 = 12/343

то есть считаем вероятности, что нам попадется каждая из разновидностей банок и перемножаем их, чтобы все события совпали.

Answer 2

Probability of Different Contents in Opened Jars

To calculate the probability of the jars having different contents, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Given that there were 3 jars with meat, 2 jars with vegetables, and 2 jars with fruits, the total number of jars is 3 + 2 + 2 = 7.

Since the labels on the jars were erased during the rain, the tourists need to open 3 jars. We want to find the probability that these 3 jars will have different contents.

To calculate the number of favorable outcomes, we can consider the different possibilities for the first jar, the second jar, and the third jar.

- For the first jar, there are 7 options. - For the second jar, there are 6 options remaining (since one jar has already been opened). - For the third jar, there are 5 options remaining.

Therefore, the number of favorable outcomes is 7 * 6 * 5 = 210.

To calculate the total number of possible outcomes, we can consider the total number of ways to choose 3 jars out of 7 without considering the order. This can be calculated using the combination formula:

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

where n is the total number of items and r is the number of items to be chosen.

In this case, we have n = 7 and r = 3, so the total number of possible outcomes is:

C(7, 3) = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35.

Therefore, the probability of the jars having different contents is:

P(different contents) = favorable outcomes / total outcomes = 210 / 35 = 6/7.

So, there is a 6/7 or approximately 0.8571 probability that the jars will have different contents when the tourists open 3 jars.

Please note that the above calculation assumes that the tourists randomly choose the jars to open and that the contents of the jars are evenly distributed.