Question

В одной коробке 20 деталей, 3 из которых бракованные, а в другой – 17 деталей, 5 из которых бракованные. Из коробок вынули по одной детали. Какова вероятность того, что обе детали хорошие?

Answer 1

17/20 * 12/17 = 0,6

Умножение т.к. первая и вторая деталь должны быть хорошими. И - логическое умножение.

Answer 2

Calculating the Probability of Drawing Two Good Parts

To calculate the probability of drawing two good parts, we can use the concept of conditional probability.

Let's denote: - A1: the event of drawing a good part from the first box - A2: the event of drawing a good part from the second box

We want to find the probability of both A1 and A2 occurring.

Calculating the Probability of Drawing a Good Part from the First Box

The probability of drawing a good part from the first box can be calculated as follows: - Total parts in the first box = 20 - Good parts in the first box = 20 - 3 = 17

So, the probability of drawing a good part from the first box is: P(A1) = (Number of good parts in the first box) / (Total parts in the first box) = 17 / 20

Calculating the Probability of Drawing a Good Part from the Second Box

Similarly, the probability of drawing a good part from the second box can be calculated as follows: - Total parts in the second box = 17 - Good parts in the second box = 17 - 5 = 12

So, the probability of drawing a good part from the second box is: P(A2) = (Number of good parts in the second box) / (Total parts in the second box) = 12 / 17

Calculating the Probability of Drawing Two Good Parts

The probability of drawing two good parts can be calculated using the formula for the probability of the intersection of independent events: P(A1 and A2) = P(A1) * P(A2) = (17 / 20) * (12 / 17)

By multiplying these probabilities, we can find the probability of drawing two good parts from the two boxes.

Result

By applying the above calculations, the probability of drawing two good parts from the two boxes is approximately 0.6353.