Question

В урне 8белых и 9 черных шаров.последовательно вынимают 3 шара.какова вероятность,что они будут чередоваться?

Answer 1

Честно говоря, не силён в сложной вероятности.
8/17*9/16*7/15=504/4080=0,12
9/17*8/16*8/15=576/4080=0,14

Answer 2

Calculating the Probability of Drawing Alternating Black and White Balls

To calculate the probability of drawing three balls in such a way that they alternate between black and white, we can use the concept of combinations and the total number of ways to draw three balls from the urn.

Total Number of Ways to Draw 3 Balls

The total number of ways to draw 3 balls from the urn of 8 white and 9 black balls can be calculated using combinations. The formula for combinations is given by: nCr = n! / (r! * (n-r)!) Where n is the total number of items, r is the number of items to choose, and ! denotes factorial.

The total number of ways to draw 3 balls from the urn is: Total ways = (8+9)C3 = 17C3

Number of Ways to Draw Alternating Black and White Balls

To calculate the number of ways to draw 3 balls such that they alternate between black and white, we can consider the following cases: 1. Black-White-Black 2. White-Black-White

Case 1: Black-White-Black

The number of ways to draw 3 balls in the sequence Black-White-Black can be calculated using combinations. The number of ways to choose 1 black ball from 9 and 2 white balls from 8 is: Ways = 9C1 * 8C2

Case 2: White-Black-White

Similarly, the number of ways to draw 3 balls in the sequence White-Black-White can be calculated using combinations. The number of ways to choose 1 white ball from 8 and 2 black balls from 9 is: Ways = 8C1 * 9C2

Calculating the Probability

The probability of drawing 3 balls in such a way that they alternate between black and white can be calculated by dividing the total number of ways to draw alternating balls by the total number of ways to draw 3 balls.

Probability = (Number of ways to draw alternating balls) / (Total number of ways to draw 3 balls)

Let's calculate the probabilities for both cases and then sum them up to get the overall probability.