Question

В корзине 3 белых ,4 красных,3 синих шарика.Мы вытаскиваем два шара . Какова вероятность того что: а) мы вытащим 1 красный и 1 синий б) хотя бы один синий.

Answer 1

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Answer 2

Probability of Drawing Balls from the Basket

Let's calculate the probability of drawing two balls from a basket containing 3 white, 4 red, and 3 blue balls.

a) Probability of Drawing 1 Red and 1 Blue Ball

The probability of drawing 1 red and 1 blue ball can be calculated using the formula: $$ P=\frac{C_{4}^1 \cdot C_{3}^1}{C_{10}^2} $$

Substituting the values: $$ P=\frac{4 \cdot 3}{45} = \frac{12}{45} = \frac{4}{15} \approx 0.267 $$

So, the probability of drawing 1 red and 1 blue ball is approximately 0.267.

b) Probability of Drawing at Least One Blue Ball

The probability of drawing at least one blue ball can be calculated by subtracting the probability of drawing no blue balls from 1. The probability of drawing no blue balls is: $$ P=\frac{C_{7}^2}{C_{10}^2} $$

Substituting the values: $$ P=\frac{21}{45} = \frac{7}{15} \approx 0.467 $$

Therefore, the probability of drawing at least one blue ball is approximately 0.533.