Question

В первой корзине 4 синих и 7 черных мяга,,во второй-8 синих и 2 черных.Из каждой корзины выбрали по 2мяча.Какова вероятность,что хотя бы из одной корзины выбрали два черных мяча?

Answer 1

Ну скорее всего потому, что в первой корзине было два чёрных мяча(моя логика)

Answer 2

Problem Analysis

We have two baskets: the first basket contains 4 blue and 7 black balls, and the second basket contains 8 blue and 2 black balls. We need to find the probability of selecting at least two black balls from either basket.

Solution

To find the probability, we need to consider two scenarios: 1. Selecting two black balls from the first basket and any combination of balls from the second basket. 2. Selecting two black balls from the second basket and any combination of balls from the first basket.

Let's calculate the probability for each scenario and then add them together to get the final probability.

Scenario 1: Selecting two black balls from the first basket

The probability of selecting two black balls from the first basket can be calculated using the formula for combinations. The number of ways to select 2 black balls from 7 is given by C(7, 2) = 21. The total number of ways to select any 2 balls from the first basket is C(11, 2) = 55.

Therefore, the probability of selecting two black balls from the first basket is 21/55.

Scenario 2: Selecting two black balls from the second basket

Similarly, the probability of selecting two black balls from the second basket can be calculated. The number of ways to select 2 black balls from 2 is given by C(2, 2) = 1. The total number of ways to select any 2 balls from the second basket is C(10, 2) = 45.

Therefore, the probability of selecting two black balls from the second basket is 1/45.

Final Probability

To find the final probability, we need to add the probabilities from both scenarios. Since we want to find the probability of selecting at least two black balls from either basket, we can use the formula for the union of events:

P(A or B) = P(A) + P(B) - P(A and B)

In this case, A represents scenario 1 and B represents scenario 2.

P(A and B) = P(selecting two black balls from the first basket) * P(selecting two black balls from the second basket) = (21/55) * (1/45)

Therefore, the final probability is:

P(A or B) = P(A) + P(B) - P(A and B) = (21/55) + (1/45) - (21/55) * (1/45)

Let's calculate the final probability.

Calculation

The final probability can be calculated as follows:

P(A or B) = (21/55) + (1/45) - (21/55) * (1/45) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475) = (21/55) + (1/45) - (1/2475