Question

A bag contains one red marble, two blue marbles and three green marbles. A marble is selected at random. Define a random variable X such that X=1 if a red marble is selected, X=2 if a blue marble is selected and X=3 if a green marble is selected. Find the following probabilities. Hint: The blue marbles are different; you can label one blue-1 and the other blue-2. Similarly, each of the green marbles is different.

4a) Find P(X=1)

4b) Find P(X=2)

4c) Find P(X=3)

4d) Draw the probability distribution of the random variable X Now assume two marbles are selected at random without replacement. That is, one marble is selected and put aside. Then another marble is selected. Let Y be the random variable that equals the sum of the two numbers corresponding to the colors of the selected marbles. That is, red corresponds to 1, blue corresponds to 2 and green corresponds to 3.

4e) List all the outcomes that result in Y=3. How many outcomes are there?

4f) List all the outcomes that result in Y=4. How many outcomes are there?

4g) List all the outcomes that result in Y=5. How many outcomes are there?

4h) List all the outcomes that result in Y=6. How many outcomes are there?

4i) For each of the possible values of Y, find the corresponding probabilities. That is, find P(Y=3), P(Y=4), P(Y=5) and P(Y=6) 4j) Draw the probability distribution of the random variable Y

Answer 1