Calculating the Probability of Selecting Orange Balls from an Urn

 An urn contains five red, three orange, and two blue balls. Two balls are randomly selected. What is the sample space of this experiment? Let X represent the number of orange balls selected. What are the possible values of X? Calculate P{X = 0}.

An urn containing five red, three orange, and two blue balls is a classic probability experiment. In this experiment, two balls are randomly selected from the urn. In this blog post, we will explore the sample space of this experiment and calculate the probability of selecting a certain number of orange balls.

The sample space of this experiment is the set of all possible outcomes when two balls are selected from the urn. There are 10 balls in the urn, so the total number of possible outcomes is 10C2, which is equal to 45. These 45 outcomes represent the different combinations of two balls that can be selected from the urn.

Let X represent the number of orange balls selected. X can take on the values of 0, 1, or 2, since it is not possible to select more than two orange balls. These are the only possible values of X.

Next, we will calculate the probability of selecting exactly 0 orange balls, P(X = 0). To do this, we will find the number of successful outcomes (when 0 orange balls are selected) and divide by the total number of possible outcomes (45).

There are 7 red and blue balls in the urn, so the number of successful outcomes (when 0 orange balls are selected) is 7C2 = 21.

Therefore, P(X = 0) = 21/45 = 7/15

In conclusion, the sample space of the experiment of randomly selecting two balls from an urn containing five red, three orange, and two blue balls is the set of all 45 possible combinations of two balls. The possible values of X, the number of orange balls selected, are 0, 1, or 2. We have also calculated P(X = 0), the probability of selecting exactly 0 orange balls, which is 7/15.