Question

1. В ящике имеется 20 изделий первого сорта и 5 изделий высшего сорта. Из ящика наугад берут 3 изделия. Какова вероятность того, что все они высшего сорта? Ребят кто нибудь помогите

Answer 1

5/20умножить4/19умножить3/18=1/57

Answer 2

Calculating the Probability of Drawing All High-Quality Items

To calculate the probability of drawing all high-quality items from the box, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Given: - There are 20 items of the first quality. - There are 5 items of the highest quality. - We are drawing 3 items from the box.

To calculate the probability, we can use the concept of combinations. The formula for combinations is:

nCr = n! / (r!(n-r)!)

Where: - n is the total number of items in the set. - r is the number of items we want to choose.

In this case, we want to calculate the probability of drawing all high-quality items, so we need to calculate the number of ways we can choose 3 items from the 5 high-quality items.

The number of ways to choose 3 items from 5 is given by:

5C3 = 5! / (3!(5-3)!) = 5! / (3!2!) = (5 * 4 * 3!) / (3! * 2 * 1) = 10

Now, we need to calculate the total number of ways we can choose 3 items from the total number of items in the box, which is 25 (20 first-quality items + 5 high-quality items).

The number of ways to choose 3 items from 25 is given by:

25C3 = 25! / (3!(25-3)!) = 25! / (3!22!) = (25 * 24 * 23!) / (3! * 22!) = 2300

Finally, we can calculate the probability by dividing the number of favorable outcomes (10) by the total number of possible outcomes (2300):

Probability = 10 / 2300 ≈ 0.0043

Therefore, the probability of drawing all high-quality items from the box is approximately 0.0043, or 0.43%.

Please note that the above calculation assumes that each item is equally likely to be drawn and that the items are drawn without replacement (i.e., once an item is drawn, it is not put back into the box before drawing the next item).