Question

В урне находится 3 белых 4 желтых и 2 черных шара. Из нее наугад вынимают (без возвращения) один за другим по одному шару. Какова вероятность того, что белый шар появится раньше желтого?

Answer 1

3-4=-1
-1+2=1
1 белый шар появится раньше желтого

Answer 2

Problem Analysis

We have an urn containing 3 white balls, 4 yellow balls, and 2 black balls. We will randomly draw one ball at a time without replacement. We need to find the probability that a white ball appears before a yellow ball.

Solution

To solve this problem, we can use the concept of permutations and combinations. Let's consider the possible outcomes when drawing the balls:

1. The first ball drawn is white (W). 2. The first ball drawn is yellow (Y), and the second ball drawn is white (W). 3. The first two balls drawn are yellow (Y), and the third ball drawn is white (W). 4. The first three balls drawn are yellow (Y), and the fourth ball drawn is white (W).

We can see that the only scenario where a white ball appears before a yellow ball is when the first ball drawn is white. Therefore, the probability of a white ball appearing before a yellow ball is equal to the probability of drawing a white ball on the first draw.

Calculation

The probability of drawing a white ball on the first draw can be calculated as follows:

Probability = (Number of white balls) / (Total number of balls)

Number of white balls = 3 Total number of balls = 3 (white) + 4 (yellow) + 2 (black) = 9

Probability = 3 / 9 = 1/3

Therefore, the probability that a white ball appears before a yellow ball is 1/3.

Answer

The probability that a white ball appears before a yellow ball is 1/3.