Question

В коробке лежат 50 электрических ламп мощностью 100 Вт и 30 мощность 60Вт . Наудачу выбирают две лампы. Найти вероятность того,что они окажуться а) одинаковой мощностью; б) разной мощностью

Answer 1

А)62,5% т.к 100:(50+30)=1.25*50=62,5%
Б)37,5% (остаток)

Answer 2

Calculating the Probability of Selecting Two Bulbs

To calculate the probability of selecting two bulbs with specific power ratings, we can use the following approach:

1. Probability of Selecting Two Bulbs of the Same Power Rating: - The probability of selecting two bulbs of the same power rating can be calculated using the formula: \[ P(\text{{same}}) = \frac{{\text{{Number of ways to choose 2 bulbs of the same power}}}}{{\text{{Total number of ways to choose 2 bulbs}}}} \] - In this case, we have 50 bulbs of 100W and 30 bulbs of 60W.

2. Probability of Selecting Two Bulbs of Different Power Ratings: - The probability of selecting two bulbs of different power ratings can be calculated using the formula: \[ P(\text{{different}}) = \frac{{\text{{Number of ways to choose 1 bulb of 100W and 1 bulb of 60W}}}}{{\text{{Total number of ways to choose 2 bulbs}}}} \]

Let's calculate these probabilities step by step.

Probability of Selecting Two Bulbs of the Same Power Rating:

The probability of selecting two bulbs of the same power rating can be calculated as follows:

\[ P(\text{{same}}) = \frac{{\text{{Number of ways to choose 2 bulbs of the same power}}}}{{\text{{Total number of ways to choose 2 bulbs}}}} \]

The total number of ways to choose 2 bulbs is given by the combination formula: \[ \text{{Total number of ways}} = \binom{80}{2} \]

The number of ways to choose 2 bulbs of the same power is the sum of combinations for 100W bulbs and 60W bulbs: \[ \text{{Number of ways to choose 2 bulbs of the same power}} = \binom{50}{2} + \binom{30}{2} \]

Let's calculate the probability.

Probability of Selecting Two Bulbs of Different Power Ratings:

The probability of selecting two bulbs of different power ratings can be calculated as follows:

\[ P(\text{{different}}) = \frac{{\text{{Number of ways to choose 1 bulb of 100W and 1 bulb of 60W}}}}{{\text{{Total number of ways to choose 2 bulbs}}}} \]

The number of ways to choose 1 bulb of 100W and 1 bulb of 60W is given by the product of the number of 100W bulbs and the number of 60W bulbs: \[ \text{{Number of ways to choose 1 bulb of 100W and 1 bulb of 60W}} = 50 \times 30 \]

Let's calculate the probability.

Results:

After calculating the probabilities, we find: - Probability of selecting two bulbs of the same power rating: - \[ P(\text{{same}}) = \frac{{\binom{50}{2} + \binom{30}{2}}}{{\binom{80}{2}}} \] - \[ P(\text{{same}}) \approx 0.493 \]

- Probability of selecting two bulbs of different power ratings: - \[ P(\text{{different}}) = \frac{{50 \times 30}}{{\binom{80}{2}}} \] - \[ P(\text{{different}}) \approx 0.507 ]

Therefore, the probabilities are approximately: - Probability of selecting two bulbs of the same power rating: 0.493 - Probability of selecting two bulbs of different power ratings: 0.507