A box contains 5 yellow balls, 3 blue, and 1 red ball. Two balls are drawn at random. Find the probability that the two balls are yellow

started with 9 balls, five of them are yellow

5/9
then we have 8 balls, four of them are yellow
1/2
so
5/9 * 1/2 = 5/18

There are 8 balls inside the box that consists of 2 blue balls and 6 yellow balls. What is the probability of getting yellow balls?

3/16

5/18

To find the probability that the two balls are yellow, you need to divide the number of favorable outcomes (drawing two yellow balls) by the number of possible outcomes.

Step 1: Determine the total number of balls in the box
Total number of balls = 5 yellow balls + 3 blue balls + 1 red ball = 9 balls

Step 2: Determine the number of ways to draw 2 yellow balls
To do this, we can use combinations. The number of combinations of drawing 2 yellow balls from 5 yellow balls can be calculated as:

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

Step 3: Determine the number of possible outcomes
The number of possible outcomes when drawing 2 balls from a total of 9 balls can be calculated as:

C(9,2) = 9! / (2! * (9-2)!) = 9! / (2! * 7!) = (9 * 8) / (2 * 1) = 36

Step 4: Calculate the probability
The probability of drawing two yellow balls can be calculated as:

Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 10 / 36 = 5 / 18

Therefore, the probability that the two balls drawn are yellow is 5/18.