A bag contains five white balls and three black balls. Your goal is to draw two black balls.
You simultaneously draw two balls at random. What is the probability that they are both black?
To find the probability that both drawn balls are black, we can use the concept of combinations.
There are a total of 8 balls in the bag - 5 white balls and 3 black balls.
To calculate the probability, we need to determine the number of favorable outcomes (drawing two black balls) and the total number of possible outcomes (drawing any two balls).
The number of favorable outcomes is obtained by selecting 2 balls from the 3 black balls. This can be represented as C(3, 2), where C denotes the combination.
C(3, 2) = 3! / (2!(3-2)!) = 3
The total number of possible outcomes is obtained by selecting 2 balls from the 8 balls. This can be represented as C(8, 2).
C(8, 2) = 8! / (2!(8-2)!) = 28
Therefore, the probability of drawing two black balls is 3/28 or approximately 0.107 or 10.7%.